Conductivity is part of Physics. Below are notes on 9 sub-topics, followed by practice MCQs from State PSC and UPSC papers.

Band Theory of Solids: Conductors, Semiconductors, and Insulators

  • Energy Bands: Electrons in solids occupy energy bands: Valence Band (VB, filled with valence electrons) and Conduction Band (CB, empty or partially filled).
  • Energy Gap (Eg): Energy difference between the top of VB and bottom of CB.
  • Conductors:
    • VB and CB overlap, or Eg ≈ 0 eV.
    • Abundant free electrons in CB for conduction.
    • Very low electrical resistance, high conductivity.
    • Examples: Metals (Copper, Aluminium, Silver, Mercury), Graphite, Human body.
  • Insulators:
    • Large Eg (> 3 eV). Electrons cannot easily jump from VB to CB.
    • Very few or no free electrons for conduction.
    • Very high electrical resistance, very low conductivity.
    • Examples: Plastic, Dry wood, Rubber, PVC, Glass, Mica, Sulphur, Diamond, Quartz, Distilled water.
  • Semiconductors:
    • Moderate Eg (0.2 eV < Eg < 3 eV).
    • Conductivity is intermediate between conductors and insulators.
    • Conductivity increases with temperature.
    • Common intrinsic semiconductors: Silicon (Si), Germanium (Ge).
    • Compound semiconductors: Gallium arsenide (GaAs), Lead sulfide (PbS), Selenium.
    • Most commonly used semiconductor: Silicon.
    • Band Gaps (approximate): Ge (0.67

GaAs has a higher band gap than Si or Ge.

  • Conductivity Order (Ascending): Insulators < Semiconductors < Conductors.
  • Specific Material Properties:
    • Graphite: Good conductor of heat and electricity (a non-metal).
    • Diamond: Good conductor of heat, but an electrical insulator (a non-metal).
    • Quartz (Silicon Dioxide): Insulator.
  • Semiconductor Devices:
    • A solar cell unit is fundamentally a semiconductor Diode.
    • The color of light emitted by an LED depends on the type of semiconductor material used.
    • Applying a forward bias to a p-n junction lowers the potential barrier.

Classical Free Electron Theory (Drude Model): Postulates, limitations, successes

  • Drude Model (Classical Free Electron Theory): Treats metals as a gas of free electrons moving within a lattice of positive ion cores.
  • Primary Conduction Mechanism: Free electrons are primarily responsible for electrical conduction in metals.
  • Postulates:
    • Valence electrons detach from atoms, becoming "free electrons."
    • Free electrons move randomly, like gas molecules (obey Maxwell-Boltzmann statistics).
    • Electrons collide only with stationary positive ion cores (elastic collisions), not with other electrons.
    • Absence of external electric field: electrons move randomly; net current is zero.
    • Presence of external electric field: electrons gain drift velocity, contributing to current.
  • Successes:
    • Successfully explains Ohm's Law (V=IR).
    • Explains electrical conductivity ($ \sigma$) and thermal conductivity (K).
    • Predicts the Wiedemann-Franz Law (K/$\sigma$T = L, where L is the Lorentz number).
    • Explains optical properties like high reflectivity of metals.
  • Limitations:
    • Specific Heat Capacity: Predicts electron contribution to specific heat as (3/2)R per mole, which is much higher than experimentally observed (due to classical Maxwell-Boltzmann statistics instead of quantum Fermi-Dirac statistics).
    • Temperature Dependence of Resistivity: Incorrectly predicts resistivity dependence on temperature; experimental values show different trends.
    • Hall Effect: Always predicts a negative Hall coefficient, but some metals (e.g., Be, Zn, Cd) exhibit a positive Hall coefficient.
    • Mean Free Path: Theoretical mean free path is significantly shorter than experimental values.
    • Fails to explain phenomena like ferromagnetism, superconductivity, and the temperature dependence of electron mean free path.
    • Ignores quantum mechanical effects and electron-electron interactions.

Dielectric properties: Dielectric constant, polarization, and dielectric breakdown (related to insulators)

  • Dielectrics: Insulators (non-conducting materials) that can sustain an external electric field. They contain no free electrons.
  • Polarization: When a dielectric is placed in an external electric field (E₀), induced or permanent molecular dipoles align, creating an internal electric field (Eᵢ) opposing E₀.
  • Net Electric Field in Dielectric: The net electric field (E) inside a dielectric is reduced due to polarization: E = E₀ - Eᵢ = E₀ / K.
  • Dielectric Constant (K or εᵣ): A dimensionless quantity representing how an electric field is reduced within a material. K = E₀/E. It is also the ratio of permittivity of the dielectric (ε) to that of free space (ε₀): K = ε/ ε₀. K ≥ 1 for all materials; K=1 for vacuum.
  • Effect of Dielectric on Capacitance:
    • Introducing a dielectric into a capacitor increases its capacitance. C = K C₀, where C₀ is capacitance without the dielectric.
    • For a parallel plate capacitor with plate area 'A', separation 'd', and a dielectric slab of thickness 't' (with dielectric constant K) partially filling the gap: C = ε₀A / [(d - t) + (t / K)].
    • If the dielectric slab fully fills the gap (t = d): C = Kε₀A / d.
  • Dielectric Strength: The maximum electric field strength an insulating material can withstand without undergoing electrical breakdown.
  • Dielectric Breakdown: Occurs when the electric field across a dielectric exceeds its dielectric strength, causing the material to lose its insulating properties and conduct current (e.g., arcing or sparking).
  • Conductors in an Electric Field: In electrostatic equilibrium, the net electric field inside the body of a conductor (including any hollow cavities within it) is zero. Electric field lines are always perpendicular to the surface of a conductor. Excess charges reside on the conductor's surface.

Electrical Conductivity and Resistivity: Definitions, Units, and Ohm's Law

  • Ohm's Law: States $V = IR$ (Voltage = Current × Resistance). Current ($I$) is directly proportional to potential difference ($V$) for ohmic materials.
  • Electrical Resistance (R):
    • Definition: Opposition to the flow of electric current.
    • SI Unit: Ohm ($\Omega$).
    • Formula: $R = \rho \frac{L}{A}$, where $\rho$ is resistivity, $L$ is length, and $A$ is cross-sectional area.
    • Dependence:
      • Directly proportional to length ($L$).
      • Inversely proportional to crosssectional area ($A$) ($R \propto 1/A$).
      • Inversely proportional to the square of diameter ($d$) ($R \propto 1/d^2$).
      • Depends on the nature of the material (resistivity, $\rho$).
      • For metallic wires, resistance generally increases as temperature rises.
  • Electrical Resistivity ($\rho$):
    • Definition: An intrinsic property of a material that quantifies its opposition to current flow, independent of its dimensions.
    • SI Unit: Ohm-meter ($\Omega$ m).
    • Dependence:
      • Depends only on the nature of the material.
      • Depends on temperature.
      • Independent of the material's length, area of cross-section, shape, or mass.
  • Electrical Conductivity ($\sigma$):
    • Definition: The reciprocal of resistivity ($\sigma = 1/\rho$). Measures how easily current flows through a material.
    • SI Unit: Siemens per meter (S/m) or ($ \Omega$ m)$^{-1}$.
    • Relationship: Higher conductivity implies lower resistivity and lower resistance for given dimensions ($R = \frac{L}{\sigma A}$).
    • Product: The product of conductivity and resistivity for any given material is always 1 ($\rho \times \sigma = 1$).
  • Material Classification by Resistivity/Conductivity:
    • Conductors: Very low resistivity, high conductivity.
      • Silver is the best electrical conductor (lowest resistivity).
      • Copper is an excellent conductor, widely used in domestic electrical wiring due to low resistance.
      • Gold, Aluminium are also good conductors.
    • Alloys: Often have higher resistivity than pure metals. Nichrome (NickelChromium alloy) has significantly higher resistivity than copper/aluminium and a high melting point, making it suitable for heating elements (e.g., electric press, heater, electric kettle).
    • Semiconductors: Intermediate resistivity. Their I-V characteristics may not be linear (non-ohmic).
    • Insulators: Very high resistivity, low conductivity. Examples include Glass and Mica.
    • Resistivity Order (increasing): Silver < Copper < Aluminium < Nichrome < Glass.
  • Static Charge Dissipation:
    • Conducting materials (e.g., conducting rubber tyres on aircraft, metallic ropes on vehicles carrying inflammable materials) are used to provide a path for static electric charge (accumulated due to friction with air or operational equipment) to safely transfer to the ground, preventing dangerous sparks.
  • Capacitance: The capacitance of a parallelplate capacitor ($C = \frac{\epsilon A}{d}$) depends on the dielectric material between the plates ($\epsilon$), the area of the plates ($A$), and the separation between them ($d$), but not on the electrical resistivity of the conductive plates themselves.

Intrinsic and Extrinsic Semiconductors: Doping, carrier concentration, and Fermi level

  • Intrinsic Semiconductors: Pure semiconductor material (e.g., Si, Ge).
  • In intrinsic semiconductors, electron-hole pairs are generated by thermal energy; electron concentration (ne) equals hole concentration (nh).
  • Extrinsic Semiconductors: Created by adding impurities (doping) to intrinsic semiconductors to increase conductivity. (MCQ 2, MCQ 8)
  • Doping significantly increases the electrical conductivity of the semiconductor. (MCQ 1, MCQ 2)
  • n-type Semiconductor: Formed by doping a pure semiconductor (e.g., Si, Ge) with pentavalent impurities (donor atoms) from Group 15 (e.g., Phosphorus (P), Arsenic (As), Antimony (Sb)). (MCQ 4, MCQ 6)
  • Pentavalent impurities have 5 valence electrons; 4 form covalent bonds, the 5th electron becomes free, increasing electron concentration. (MCQ 4)
  • In n-type semiconductors, electrons are the majority charge carriers, and holes are the minority charge carriers.
  • The Fermi level in n-type semiconductors shifts closer to the conduction band.
  • An n-type semiconductor is electrically neutral, as the added donor atoms are neutral. (MCQ 7)
  • p-type Semiconductor: Formed by doping a pure semiconductor (e.g., Si, Ge) with trivalent impurities (acceptor atoms) from Group 13 (e.g., Boron (B), Aluminum (Al), Gallium (Ga), Indium (In)). (MCQ 1)
  • Trivalent impurities have 3 valence electrons, creating a 'hole' in the crystal lattice to complete covalent bonding, increasing hole concentration.
  • In p-type semiconductors, holes are the majority charge carriers, and electrons are the minority charge carriers. (MCQ 3)
  • The Fermi level in p-type semiconductors shifts closer to the valence band.
  • A p-type semiconductor is electrically neutral.
  • Carrier Concentration:
    • Intrinsic: ne = nh = ni (intrinsic carrier concentration).
    • n-type: ne >> nh (ne ≈ ND, donor impurity concentration).
    • p-type: nh >> ne (nh ≈ NA, acceptor impurity concentration).
  • Electric conduction in all semiconductors (intrinsic and extrinsic) occurs due to the movement of both electrons and holes. (MCQ 5)

Ionic Conductivity: Mechanisms in solids and liquids

  • Ionic conductivity is the electrical conduction due to the movement of ions.
  • It contrasts with electronic conductivity, which involves the movement of electrons.
  • Mechanism in Liquids:
    • Requires the presence of free, mobile ions.
    • Ions migrate towards electrodes of opposite polarity under an applied electric field.
    • Good ionic conductors: Molten salts, aqueous solutions of electrolytes (acids, bases, salts).
      • Examples: Salted water (Na+, Cl-), lemon juice (H+, citrate ions from citric acid), orange juice (H+, citrate, ascorbate, mineral ions).
    • Bad ionic conductors: Pure/distilled water (very low concentration of H+, OH- ions), non-polar liquids, and covalent liquids that do not ionize.
  • Mechanism in Solids (Solid Electrolytes / Superionic Conductors):
    • Requires a crystal lattice with defects (vacancies or interstitial sites) allowing ion movement.
    • Vacancy mechanism: An ion moves from its lattice site into an adjacent vacant site.
    • Interstitial mechanism: An ion moves from one interstitial site to another.
    • Typically occurs at elevated temperatures or in materials with specific open crystal structures.
    • Examples: Beta-alumina (Na+ conductor), silver iodide (Ag+ conductor), yttria-stabilized zirconia (O2- conductor).
    • Applications include solid-state batteries, fuel cells, and sensors.
  • Factors Affecting Ionic Conductivity:
    • Temperature: Generally increases with temperature due to increased thermal energy facilitating ion movement and defect formation.
    • Concentration (in liquids): Increases with the concentration of mobile ions up to an optimal point.
    • Viscosity (in liquids): Decreases with increasing viscosity as it hinders ion mobility.
    • Ion Mobility: Depends on the ion's size, charge, and interactions with the solvent or crystal lattice.

Superconductivity: Basic phenomena, Meissner effect, Type I and Type II superconductors

  • Superconductivity Basic Phenomena: Materials exhibiting zero electrical resistance below a characteristic critical temperature (Tc).
  • Discovered by H. Kamerlingh Onnes (1911) in Mercury.
  • Transition from normal to superconducting state is sharp.
  • Superconductors also exhibit perfect diamagnetism.
  • Meissner Effect: Complete expulsion of magnetic field lines from the interior of a superconductor when cooled below Tc in a weak external magnetic field.
  • Superconductors become perfect diamagnets (magnetic induction B=0 inside).
  • Distinguishes superconductors from ideal conductors, which would trap flux.
  • Type I Superconductors (Soft Superconductors):
  • Typically pure metals (e.g., Al, Pb, Hg, Sn).
  • Exhibit a single critical magnetic field (Hc); superconductivity is completely destroyed above Hc.
  • Show complete Meissner effect below Hc.
  • Generally have low critical fields (Hc).
  • Type II Superconductors (Hard Superconductors):
  • Typically alloys and ceramic compounds (e.g., Nb-Ti, Nb₃Sn, YBa₂Cu₃O₇).
  • Exhibit two critical magnetic fields: Hc1 (lower) and Hc2 (upper).
  • Below Hc1: Complete Meissner effect (perfect diamagnetism, B=0 inside).
  • Between Hc1 and Hc2 (Vortex/Mixed State): Magnetic field penetrates as quantized flux vortices, but the bulk material remains superconducting. Partial Meissner effect.
  • Above Hc2: Superconductivity is completely destroyed.
  • Generally have high critical fields (Hc2) and high critical temperatures (Tc).
  • YBa₂Cu₃O₇ (YBCO) is a prominent high-Tc Type II superconductor with high critical temperature and critical magnetic flux density.

Temperature dependence of conductivity in metals and semiconductors

  • Metals/Conductors:
  • Resistance increases with increasing temperature.
  • Resistivity increases with increasing temperature.
  • Conductivity decreases with increasing temperature.
  • Have a positive temperature coefficient of resistance (e.g., Copper).
  • Reason: Increased thermal vibrations scatter free electrons more, reducing their mobility.
  • Semiconductors (Pure):
  • Resistance decreases with increasing temperature.
  • Resistivity decreases with increasing temperature.
  • Conductivity increases with increasing temperature.
  • Have a negative temperature coefficient of resistance (e.g., Carbon, Germanium, Silicon).
  • Reason: Increased temperature generates more free charge carriers (electrons and holes), which outweighs the effect of reduced mobility due to scattering.
  • Silicon, a semiconductor, improves as a conductor with rising temperature but is permanently damaged around 150°C.

Thermal Conductivity: Mechanisms and Wiedemann-Franz Law

  • Thermal conductivity (k) quantifies a material's ability to conduct heat. Higher k signifies a better conductor.
  • Mechanisms of Heat Conduction:
    • Metals: Primarily via free electrons (dominant contribution) and lattice vibrations (phonons).
    • Non-metals/Insulators: Primarily via lattice vibrations (phonons).
    • Liquids & Gases: Through molecular collisions and diffusion.
  • Wiedemann-Franz Law: For metals, the ratio of thermal conductivity (k) to electrical conductivity (σ) is directly proportional to the absolute temperature (T). Formula: `k / (σT) = L` (Lorentz number). This law indicates that good electrical conductors are also generally good thermal conductors.
  • General Order of Thermal Conductivity (Descending): Metals > Alloys > Semiconductors > Liquids > Non-metals/Insulators > Gases.
  • Excellent Thermal Conductors (Metals): Silver and Copper are among the best thermal conductors (Silver > Copper).
  • Specific Material Comparisons:
    • Steel > Water > Wood: This is the correct order of thermal conductivity for these materials.
    • Diamond: Possesses exceptionally high thermal conductivity at room temperature (due to efficient phonon transport through strong covalent bonds), but is an electrical insulator (low electrical conductivity).
    • Ice: Is a poor conductor of heat. Its accumulation inside a refrigerator adversely affects cooling efficiency.
    • Mercury: A liquid metal, generally has lower thermal conductivity than solid metals like copper, silver, zinc, or lead. Lead is generally a poorer conductor than copper, silver, or zinc.
    • Alloys: Typically exhibit lower thermal conductivity than their constituent pure metals due to increased scattering of electrons and phonons.
    • Semiconductors: Have thermal conductivities intermediate between metals and insulators.
    • Superconductors: While offering zero electrical resistance at critical temperatures, their thermal conductivity varies and is generally not the lowest compared to alloys or semiconductors.
  • Gases: Generally possess very low thermal conductivity.
    • Hydrogen: Has the highest thermal conductivity among common gases due to its low molecular mass and high molecular speed.
    • Order (Descending k): Hydrogen > Helium > Air (Nitrogen, Oxygen) > Carbon dioxide.

12. Nuclear Physics

Practice MCQs: Conductivity

Band Theory of Solids: Conductors, Semiconductors, and Insulators

  1. Which one of the following is not a semiconductor?

    Asked in: UPSC CDS 1 2017

    1. Silicon
    2. Germanium
    3. Quartz
    4. Gallium arsenide
    Show answer

    Answer: C. Quartz

    Semiconductors are materials with electrical conductivity between that of a conductor and an insulator. Silicon (Si) and Germanium (Ge) are elemental semiconductors. Gallium arsenide (GaAs) is a compound semiconductor. Quartz is primarily silicon dioxide (SiO₂), which is an excellent electrical insulator.

  2. Which one of the following is an electric conductor ?

    Asked in: UPSC CDS 1 2021

    1. A plastic sheet
    2. Distilled water
    3. Human body
    4. A wooden thin sheet
    Show answer

    Answer: C. Human body

    Conductors allow charge flow, insulators resist it. The presence of free charge carriers (like ions in solutions or free electrons in metals) determines conductivity.

  3. Which one of the following semi-conductors possesses the highest value of band gap Eg?

    Asked in: UPSC Geoscientist 2023

    1. Si
    2. Ge
    3. GaAs
    4. PbS
    Show answer

    Answer: C. GaAs

    The band gap is the energy difference between the top of the valence band and the bottom of the conduction band. This value is a key characteristic of semiconductor materials.

  4. Consider the following : (a) Mica (b) Graphite (c) Sulphur (d) Human body Which among the above is/are electrical conductors?

    Asked in: KPSC KAS Prelims 2024

    1. Only (a), (b) and (d)
    2. Only (b), (c) and (d)
    3. Only (b) and (d)
    4. Only (b)
    Show answer

    Answer: C. Only (b) and (d)

    Let's evaluate the electrical conductivity of each material: (a) Mica: Mica is an excellent electrical insulator. (b) Graphite: Graphite, a form of carbon, is a good electrical conductor due to the delocalized electrons in its layered structure. (c) Sulphur: Sulphur is a non-metal and an electrical insulator. (d) Human body: The human body contains water and ions, which allows it to conduct electricity.

  5. Which one of the following statements is correct with regard to the material of electrical insulators ?

    Asked in: UPSC NDA 1 2017

    1. They contain no electrons
    2. Electrons do not flow easily through them
    3. They are crystals
    4. They have more number of electrons than the protons on their surface
    Show answer

    Answer: B. Electrons do not flow easily through them

    Electrical insulators are materials characterized by their high resistance to the flow of electric current. This property arises because the electrons in these materials are tightly bound to the atoms and are not free to move readily under the influence of an electric field.

  6. The substance which has a large number of free electrons and offer a low resistance is called :

    Asked in: UKPSC CS Prelims 2021

    1. Insulator
    2. Inductor
    3. Conductor
    4. Semi-conductor
    Show answer

    Answer: C. Conductor

    - Conductors have many free charge carriers (usually electrons in solids). - Free electrons facilitate the flow of electric current. - Low resistance means high conductivity.

  7. What is the correct sequence of conductivity when arranged in ascending order?

    Asked in: UPSC CAPF 2013

    1. Metals, semiconductors, insulators
    2. Insulators, metals, semi-conductors
    3. Semiconductors, metals, insulators
    4. Insulators, semiconductors, metals
    Show answer

    Answer: D. Insulators, semiconductors, metals

    Electrical conductivity is a measure of a material's ability to conduct electric current. Materials are classified based on their conductivity: - Insulators have very low conductivity, resisting the flow of charge (e.g., rubber, plastic, glass). - Semiconductors have conductivity between that of insulators and conductors, which can be significantly altered by temperature, doping, or external fields (e.g., silicon, germanium). - Metals (conductors) have high conductivity, allowing charge to flow easily (e.g., copper, silver, gold). Arranging these in ascending order of conductivity means starting from the lowest conductivity to the highest. Therefore, the correct sequence is Insulators

  8. Which of the following elements is a semiconductor?

    Asked in: WBCS Main Paper 4 2021

    1. Aluminium
    2. Mercury
    3. Silicon
    4. Silver
    Show answer

    Answer: C. Silicon

    Semiconductors have conductivity between conductors and insulators. Silicon and Germanium are common elemental semiconductors. Aluminium, Mercury, and Silver are conductors.

  9. Consider the following statements and choose the correct ones using the codes given below : A. Graphite is good conductor of heat & electricity. B. Graphite is good conductor of heat but an electrical insulator. C. Diamond is good conductor of heat but an electrical insulator. D. Diamond is bad conductor of heat & electricity. Codes :

    Asked in: ACF And Forest Range Officer Gr I Comp. Exam 2018

    1. A and D
    2. A and C
    3. B and C
    4. B and D
    Show answer

    Answer: B. A and C

    Graphite is a good conductor of heat and electricity. Diamond is a good conductor of heat but an electrical insulator.

  10. Which of the following allow the electric current to pass through it : A) Glasses B) Graphite C) Rubber D) PVC

    Asked in: ASSISTANT AUDIT OFFICER 2017 18 2017

    1. Glasses
    2. Graphite
    3. Rubber
    4. PVC
    Show answer

    Answer: B. Graphite

    Graphite is a conductor of electricity among the given options.

  11. A solar cell unit is basically a :

    Asked in: Assistant Engineer (AE) Exam 2013

    1. A semiconductor Triode
    2. A semiconductor Diode
    3. A Junction between two good conductors
    4. None of the above
    Show answer

    Answer: B. A semiconductor Diode

    A solar cell operates based on the photovoltaic effect, which is enabled by a p-n junction in a semiconductor material.

Classical Free Electron Theory (Drude Model): Postulates, limitations, successes

  1. Which one of the following is primarily responsible for conduction of current in a metal ?

    Asked in: UPSC NDA 1 2024

    1. Bound electrons
    2. Free electrons
    3. Both bound and free electrons
    4. Ions
    Show answer

    Answer: B. Free electrons

    - Electrical current in conductors is the flow of charge carriers. - In metals, the charge carriers are free electrons. - Free electrons are valence electrons that are not bound to individual atoms and can move throughout the material.

Dielectric properties: Dielectric constant, polarization, and dielectric breakdown (related to insulators)

  1. Which one among the following is the correct representation of the electric field when a conducting spherical shell is placed between the plates of a parallel plate capacitor ?

    Asked in: UPSC Geoscientist 2024

    1. Diagram (a)
    2. Diagram (b)
    3. Diagram (c)
    4. Diagram (d)
    Show answer

    Answer: C. Diagram (c)

    Inside a conductor in electrostatic equilibrium, the electric field is zero. Electric field lines must be perpendicular to the surface of a conductor. In a parallel plate capacitor, the field is uniform between the plates in the absence of the sphere. When a conducting sphere is introduced, induced charges on its surface redistribute the field lines.

  2. An ebonite plate (K = 3), 6 mm thick, is introduced between the parallel plates of a capacitor of plate area 2 × 10⁻² m² and plate separation is 0.01 m. The capacitance of the capacitor would be (ε₀ = 8.85 × 10⁻¹² F/m)

    Asked in: Co operative Supervisor & Environment Supervisor (Group C) Exam 2023

    1. 2.95 pF
    2. 29.5 pF
    3. 0.295 pF
    4. 29.5 µF
    Show answer

    Answer: B. 29.5 pF

    When a dielectric material with dielectric constant K is introduced into a capacitor, its capacitance increases. If the dielectric completely fills the space between the plates, the new capacitance is C' = K C, where C is the original capacitance. If a dielectric slab of thickness 't' is inserted into a capacitor with plate separation 'd', the new capacitance is given by C' = (ε₀ A) / (d - t + t/K).

Electrical Conductivity and Resistivity: Definitions, Units, and Ohm's Law

  1. A parallel-plate capacitor of capacitance C₁ is made using two gold plates. Another parallel- plate capacitor of capacitance C₂ is made using two aluminium plates with same plate separation, and all the four plates are of same area. If ρg and ρa are respectively resistivities of gold and aluminium, then which one of the following relations is correct?

    Asked in: UPSC CDS 1 2017

    1. C₁ > C₂
    2. C₂ > C₁
    3. C₁ρa = C₂ρg
    4. C₁ = C₂
    Show answer

    Answer: D. C₁ = C₂

    - The problem states that both capacitors have the same plate separation (d) and the four plates are of the same area (meaning the plates for C₁ have area A, and the plates for C₂ also have area A). - The plates are made of gold and aluminium. These materials are conductors and form the plates; they are not the dielectric material filling the space between the plates. The dielectric material between the plates is presumably the same for both capacitors (usually air or vacuum unless specified otherwise). - Since A, d, and the dielectric material (and thus its permittivity ε) are the same for both capacitors, their capacitances must be equal. - The resistivities of gold (ρg) and aluminium (ρa) are properties of the plate materials themselves and do not affect the capacitance value, which is determined by the geometry of the plates and the material between them.

  2. Two metallic wires made from copper have same length but the radius of wire 1 is half of that of wire 2. The resistance of wire 1 is R. If both the wires are joined together in series, the total resistance becomes

    Asked in: UPSC CDS 1 2018

    1. 2R
    2. R/2
    3. 5R/4
    4. 3R/4
    Show answer

    Answer: C. 5R/4

    - Resistance is inversely proportional to the square of the radius (R ∝ 1/r²), assuming constant length and material. - When conductors are in series, their resistances add up (R_total = R1 + R2 + ...).

  3. We are given three copper wires of different lengths and different areas of cross-section. Which one of the following would have highest resistivity ?

    Asked in: UPSC CDS 1 2021

    1. Copper wire of 50 cm length and 1 mm dia‐ meter
    2. Copper wire of 25 cm length and 0.5 mm diameter
    3. Copper wire of 10 cm length and 2.0 mm diameter
    4. All the wires would have same resistivity
    Show answer

    Answer: D. All the wires would have same resistivity

    - The resistance (R) of a wire is given by the formula R = ρ (L/A), where ρ is the resistivity, L is the length, and A is the area of cross-section. - While the resistance (R) of the copper wires will be different because they have different lengths and diameters, their resistivity (ρ) will be the same because they are all made of the same material (copper) and are presumably at the same temperature.

  4. What is the correct sequence of resistivity of silver, nichrome and glass at room temperature ?

    Asked in: UPSC CDS 1 2022

    1. Silver < Nichrome < Glass
    2. Glass < Nichrome < Silver
    3. Silver < Glass < Nichrome
    4. Nichrome < Silver < Glass
    Show answer

    Answer: A. Silver < Nichrome < Glass

    Good electrical conductors have very low resistivity. Metals like silver are excellent conductors. Alloys like nichrome are generally poorer conductors than pure metals and have higher resistivity. Insulators have very high resistivity, effectively preventing current flow. Glass is a good insulator. Therefore, the correct order of resistivity from lowest to highest is Silver (conductor)

  5. Two wires are made having same length l and area of cross-section A. Wire 1 is made of copper and wire 2 is made of aluminium. It is given that the electrical conductivity of copper is more than that of aluminium. In this context, which one of the following statements is correct?

    Asked in: UPSC CDS 2 2017

    1. The resistance of wire 1 will be higher than that of wire 2.
    2. The resistance of wire 2 will be higher than that of wire 1.
    3. The resistance of both the wires will be the same.
    4. If same current is flown through both the wires, the power dissipated in both the wires will be the same.
    Show answer

    Answer: B. The resistance of wire 2 will be higher than that of wire 1.

    The resistance (R) of a wire is inversely proportional to its electrical conductivity (σ) for a given length (l) and area of cross-section (A). The formula is R = (1/σ) (l/A). Since both wires have the same length and area of cross-section, their resistances are directly proportional to their resistivities (ρ = 1/σ). We are given that the electrical conductivity of copper (wire 1) is more than that of aluminium (wire 2), i.e., σ_Cu > σ_Al. This implies that the resistivity of copper is less than that of aluminium (ρ_Cu

  6. A metal wire of length l and diameter d has a resistance R. What would be the resistance of another wire of the same metal and of same length but having double the diameter ?

    Asked in: UPSC CDS 2 2022

    1. R
    2. R/4
    3. R/2
    4. 2R
    Show answer

    Answer: B. R/4

    - Resistance is inversely proportional to the cross-sectional area of the wire. - Cross-sectional area is proportional to the square of the diameter.

  7. Which one of the following is the most appropriate reason for aircraft being equipped with conducting tyres ?

    Asked in: UPSC CDS 2 2024

    1. They can transfer the charge accumulated on their surfaces during lightning
    2. They can transfer the charge accumulated on their surfaces being rubbed by air particles
    3. They can transfer accumulated on their surfaces due to inflight operation of several gadgets
    4. For preventing sparks on the ground while they land
    Show answer

    Answer: D. For preventing sparks on the ground while they land

    Aircraft build up a considerable amount of static electric charge during flight due to friction with air, dust, and precipitation. This charge needs to be safely dissipated upon landing. Conducting tyres provide a low-resistance path for this accumulated static charge to flow from the aircraft's structure to the ground, thus neutralizing the charge gradually and preventing a sudden electrostatic discharge or spark that could ignite flammable fuel vapours near the ground.

  8. The electrical resistance of a wire varies directly with its length and inversely with the square of its diameter. If a wire with a length of 200 cm and a diameter of one-quarter of a centimeter has a resistance of 20 ohms, find the electrical resistance in a 500 cm wire with the same diameter

    Asked in: GPSC Prelims CSP 1 2018

    1. 25 ohms
    2. 40 ohms
    3. 50 ohms
    4. None of the above
    Show answer

    Answer: C. 50 ohms

    - Establish the relationship between resistance, length, and diameter using a constant of proportionality. - Use the given initial conditions to find the constant $k$. - Use the constant $k$ and the new dimensions to calculate the new resistance.

  9. The product of conductivity and resistivity of a conductor

    Asked in: UPSC NDA 1 2015

    1. depends on pressure applied
    2. depends on current flowing through con‐ ductor
    3. is the same for all conductors
    4. varies from conductor to conductor
    Show answer

    Answer: C. is the same for all conductors

    By definition, conductivity is the reciprocal of resistivity ($\sigma = 1/\rho$). Therefore, the product of conductivity and resistivity is always equal to 1 ($\sigma \times \rho = (1/\rho) \times \rho = 1$). This relationship holds true for all materials, regardless of whether they are conductors, insulators, or semiconductors, and it is independent of the physical conditions like pressure or the current flowing through the conductor (assuming the material obeys Ohm's Law).

  10. Which one of the following correctly represents the SI unit of resistivity?

    Asked in: UPSC NDA 1 2022

    1. $\Omega$
    2. $\Omega$/m
    3. $\Omega$ cm
    4. $\Omega$ m
    Show answer

    Answer: D. $\Omega$ m

    Resistivity ($\rho$) is an intrinsic property of a material that quantifies how strongly it resists electric current. It is related to resistance ($R$), length ($L$), and cross-sectional area ($A$) of a conductor by the formula $R = \rho \frac{L}{A} $.

  11. Why are the tyres of aircrafts made of conducting rubber? 1. So that the charge accumulated on the aircraft in flight, by rubbing the air, can easily be transferred to ground on landing. 2. So that the charge accumulated due to the operation of various electronic equipments in the aircraft in flight can easily be transferred to ground on landing. Select the correct answer using the code given below.

    Asked in: UPSC NDA 1 2022

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Show answer

    Answer: C. Both 1 and 2

    Aircraft accumulate static electric charge during flight due to friction with air (triboelectric effect) and the operation of onboard electronic equipment.

Intrinsic and Extrinsic Semiconductors: Doping, carrier concentration, and Fermi level

  1. When a piece of pure silicon is doped with aluminium, then

    Asked in: UPSC CDS 1 2017

    1. the conductivity of the doped silicon piece will remain the same
    2. the doped silicon piece will become n-type
    3. the doped silicon piece will become p-type
    4. the resistivity of the doped silicon piece will increase
    Show answer

    Answer: C. the doped silicon piece will become p-type

    Pure silicon is a semiconductor with a valence of four. Aluminium is a Group 13 element and acts as a trivalent impurity (valence of three) when doped into silicon. When a trivalent impurity replaces a silicon atom in the crystal lattice, it creates a 'hole' (absence of an electron) in the covalent bond structure. These holes act as positive charge carriers, making the doped semiconductor p-type.

  2. Suitable impurities are added to a semiconductor depending on its use. This is done in order to

    Asked in: KPSC KAS Prelims 2014

    1. increase its life
    2. enable it to withstand higher voltages
    3. increase its electrical conductivity
    4. increase its electrical resistivity
    Show answer

    Answer: C. increase its electrical conductivity

    Doping is the process of intentionally introducing impurities into an intrinsic semiconductor for the purpose of modulating its electrical properties, specifically increasing its conductivity.

  3. The majority charge carriers in a p-type semiconductor are

    Asked in: UPSC NDA 2 2017

    1. free electrons
    2. conduction electrons
    3. ions
    4. holes
    Show answer

    Answer: D. holes

    - P-type semiconductors are created by doping with trivalent impurities. - Trivalent impurities create electron deficiencies called holes. - Holes act as positive charge carriers. - In p-type semiconductors, holes are the majority charge carriers.

  4. The valence electron of the impurity atom that is to be added to germanium crystal so as to make it a n-type semiconductor is

    Asked in: TNPSC CS Prelims 2017

    1. 6
    2. 5
    3. 4
    4. 3
    Show answer

    Answer: B. 5

    - Germanium is a Group 14 semiconductor with 4 valence electrons. - n-type semiconductors are created by doping with donor impurities. - Donor impurities have more valence electrons than the semiconductor material. - For Germanium (4 valence electrons), Group 15 elements (pentavalent, 5 valence electrons) are used as donors.

  5. Electric conduction in a semiconductor takes place due to

    Asked in: UKPSC CS Prelims 2016

    1. Electrons only
    2. Holes only
    3. Both electrons and holes
    4. Neither electrons nor holes
    Show answer

    Answer: C. Both electrons and holes

    In semiconductors, electrical current can be carried by two types of charge carriers: negatively charged electrons moving in the conduction band, and positively charged "holes" (which represent the absence of an electron) moving in the valence band.

  6. In N-type semiconductor, ultrapure Si is doped with

    Asked in: WBCS Main Paper 4 2022

    1. Boron
    2. Aluminum
    3. Phosphorous
    4. Indium
    Show answer

    Answer: C. Phosphorous

    When a pentavalent atom like Phosphorous replaces a Silicon atom in the crystal lattice, four of its valence electrons form covalent bonds with neighboring Silicon atoms. The fifth valence electron is loosely bound and becomes a free electron that can easily move and contribute to electrical conductivity. These free electrons are the majority charge carriers in an N-type semiconductor.

  7. An n-type semiconductor is

    Asked in: WBCS Main Paper 4 2023

    1. negatively charged.
    2. positively charged.
    3. neutral.
    4. negatively or positively charged depending upon the amount and substance of impurity.
    Show answer

    Answer: C. neutral.

    An n-type semiconductor is created by doping a pure semiconductor crystal with donor impurity atoms. These donor atoms contribute extra electrons, which become mobile charge carriers. However, the crystal as a whole remains electrically neutral because the positive charges associated with the fixed donor ions are balanced by the total charge of the electrons and the atoms of the base semiconductor.

  8. When a small amount of a suitable impurity is added to the pure elemental semiconductor, the conductivity of the semiconductor is increased manifold. Such materials are known as - - (5) Question not attempted

    Asked in: Protection Officer 2024

    1. Extrinsic semiconductors
    2. Compound semiconductors
    3. Dopants
    4. Intrinsic semiconductors
    Show answer

    Answer: A. Extrinsic semiconductors

    Extrinsic semiconductors are created by doping intrinsic semiconductors with impurities to increase their electrical conductivity.

Ionic Conductivity: Mechanisms in solids and liquids

  1. Which of the following liquids is a bad conductor of electricity?

    Asked in: BPSC Prelims Exam 69th

    1. Salted water
    2. Orange juice
    3. Lemon juice
    4. None of the above
    Show answer

    Answer: D. None of the above

    - Conductivity in liquids containing water is due to the presence of dissolved ions. - Electrolytes (substances that produce ions when dissolved) make a liquid a good conductor. - Salted water, orange juice, and lemon juice all contain electrolytes.

Superconductivity: Basic phenomena, Meissner effect, Type I and Type II superconductors

  1. are materials whose resistivities become zero below a critical temperature.

    Asked in: MPSC CS Prelims 2023

    1. Conductors
    2. Insulators
    3. Super conductors
    4. None of these
    Show answer

    Answer: C. Super conductors

    The defining characteristic of a superconductor is zero electrical resistivity below its critical temperature, along with the expulsion of magnetic fields (Meissner effect).

  2. Superconductors are substances which

    Asked in: WBPSC CS Prelims 2020

    1. conduct electricity at lower temperature.
    2. offer high resistance to the flow of current.
    3. offer no resistance to the flow of current.
    4. conduct electricity at high temperature.
    Show answer

    Answer: C. offer no resistance to the flow of current.

    Superconductors offer no resistance to the flow of electric current below their critical temperature.

  3. Which of the following super conducting material has the highest critical temperature and highest critical magnetic flux density?

    Asked in: WBCS Main Paper 4 2022

    1. Lead
    2. Nb-Zr alloy
    3. Nb₃Ge
    4. YBa₂Cu₃O₇
    Show answer

    Answer: D. YBa₂Cu₃O₇

Temperature dependence of conductivity in metals and semiconductors

  1. On heating, the resistance of a semiconductor

    Asked in: BPSC Prelims Exam 66th UPPSC Upper Mains 2015

    1. increases
    2. decreases
    3. remains same
    4. first increases and then decreases
    Show answer

    Answer: B. decreases

    Semiconductors have a negative temperature coefficient of resistance; their resistance decreases with increasing temperature.

  2. Silicon is one of the best known semi conducting material. As its temperature rises more, it becomes a better conductor. But the temperature at which the silicon gets permanently damaged is

    Asked in: TNPSC CS Prelims 2021

    1. 100°C
    2. 150°C
    3. 200°C
    4. 250°C
    Show answer

    Answer: B. 150°C

    Silicon semiconductor devices are typically rated for a maximum junction operating temperature. Exceeding this temperature can lead to permanent damage, such as diffusion of dopants, breakdown of insulating layers, or thermal runaway, which results in irreversible changes to the device's structure and characteristics. For standard silicon devices (like those based on bipolar junctions or CMOS technology), the maximum allowable junction temperature is commonly around 150°C.

  3. With increase in temperature the resistance of a pure semiconductor

    Asked in: WBPSC CS Prelims 2016

    1. first increases and then decreases.
    2. remains the same.
    3. increases.
    4. decreases.
    Show answer

    Answer: D. decreases.

    In pure semiconductors, the number of free charge carriers (electrons and holes) increases significantly with increasing temperature due to the breaking of covalent bonds. Although lattice vibrations (which impede carrier movement) also increase with temperature, the exponential increase in charge carrier concentration is the dominant factor, leading to a decrease in resistivity and thus resistance.

  4. Electrical resistivity of a conductor

    Asked in: WBCS Main Paper 4 2022

    1. increases with temperature
    2. decreases with temperature
    3. does not change with temperature
    4. decreases at lower temperature, then increases with temperature
    Show answer

    Answer: A. increases with temperature

    - Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. - In metallic conductors, electrical conduction is primarily due to the movement of free electrons. - As temperature increases, the atoms within the conductor vibrate more vigorously around their lattice positions. These increased vibrations make it more likely for the free electrons to collide with the vibrating atoms, scattering the electrons and impeding their flow. - This increased scattering leads to a higher resistance and thus higher resistivity at higher temperatures.

  5. The positive temperature coefficient of resistance is for

    Asked in: WBCS Main Paper 4 2023

    1. Carbon
    2. Germanium
    3. Copper
    4. An electrolyte
    Show answer

    Answer: C. Copper

    Most metals have a positive temperature coefficient of resistance. As temperature increases, the thermal vibrations of the atoms increase, which scatters the conducting electrons more frequently, thus increasing resistance. Copper is a metal.

Thermal Conductivity: Mechanisms and Wiedemann-Franz Law

  1. The poorest conductor of heat among the following is

    Asked in: BPSC Prelims Exam 66th

    1. copper
    2. lead
    3. mercury
    4. zinc
    Show answer

    Answer: C. mercury

    Mercury is a poor conductor of heat compared to most other metals listed.

  2. Which one of the following pairs of metals are very good conductors of heat ?

    Asked in: UPSC CDS 2 2022

    1. Silver and Copper
    2. Silver and Lead
    3. Copper and Mercury
    4. Lead and Mercury
    Show answer

    Answer: A. Silver and Copper

    Silver and Copper are excellent conductors of heat.

  3. Which among the following has the least thermal conductivity?

    Asked in: OPSC CS Prelims 2023

    1. metal
    2. semiconductor
    3. superconductor
    4. alloy
    Show answer

    Answer: B. semiconductor

    - Thermal conductivity indicates how efficiently heat passes through a material. - Metals are good conductors, insulators are poor conductors. - Semiconductors fall between conductors and insulators.

  4. In terms of thermal conductivity (k) and electrical conductivity (δ), diamond has

    Asked in: WBPSC CS Prelims 2021

    1. low k and high δ
    2. high k and low δ
    3. high k and high δ
    4. low k and low δ
    Show answer

    Answer: B. high k and low δ

    Diamond possesses the highest thermal conductivity of any known bulk material at room temperature but is an electrical insulator.

  5. Consider the following statements: Assertion (A): If Ice collects on the freeze the cooling in the refrigerator is affected adversely. Reason (R) : Ice is a poor conductor. Select the correct answer using the codes given below: Codes:

    Asked in: UPPCS Prelims 2010

    1. Both (A) and (R) are true and (R) is the correct explanation of (A).
    2. Both (A) and (R) are true, but (R) is not the correct explanation of (A).
    3. (A) is true, but (R) is false.
    4. (A) is false, but (R) is true.
    Show answer

    Answer: A. Both (A) and (R) are true and (R) is the correct explanation of (A).

    Assertion (A) states that ice collection on a freezer adversely affects cooling. This is true because ice acts as an insulator, impeding the transfer of cold from the cooling coils to the interior of the freezer. Reason (R) states that ice is a poor conductor. This is also true; ice is a relatively poor thermal conductor compared to the materials typically used for freezer walls and cooling coils.

  6. Which one among the following statements about thermal conductivity is correct? [A] Steel > Wood > Water [B] Steel > Water > Wood [C] Water > Steel > Wood [D] Wood > Water > Steel

    Asked in: ASCO 2014

    1. [A] Steel > Wood > Water
    2. [B] Steel > Water > Wood
    3. [C] Water > Steel > Wood
    4. [D] Wood > Water > Steel
    Show answer

    Answer: B. [B] Steel > Water > Wood

    HORTICULTURE DEVELOPMENT OF‐ FICER(HDO) -2015 Thermal conductivity ranks materials based on their heat conduction ability. Metals are generally excellent conductors, liquids are moderate, and non-metals/insulators are poor conductors. Steel (metal) has high conductivity, water has moderate conductivity, and wood has low conductivity.

  7. Which one among the following statements about thermal conductivity is correct? [A] Steel > Wood [B] Steel > Water [C] Water > Steel > Wood [D] Water > Wood > Steel

    Asked in: HORTICULTURE DEVELOPMENT OF‐ FICER(HDO) 2015

    1. Steel > Wood
    2. Steel > Water
    3. Water > Steel > Wood
    4. Water > Wood > Steel
    Show answer

    Answer: A. Steel > Wood

    HORTICULTURE DEVELOPMENT OF‐ FICER(HDO) -2015 Thermal conductivity measures how well a material transfers heat. Metals are excellent conductors, while insulators (like wood) are poor conductors.

  8. Which one among the following statements about thermal conductivity is correct? [A] Steel > Wood > Water [B] Steel > Water > Wood [C] Water > Steel > Wood [D] Wood > Water > Steel

    Asked in: HORTICULTURE DEVELOPMENT OF‐ FICER(HDO) 2015 · POST GRADUATE TEACHER (PGT) 2018

    1. [A] Steel > Wood > Water
    2. [B] Steel > Water > Wood
    3. [C] Water > Steel > Wood
    4. [D] Wood > Water > Steel
    Show answer

    Answer: B. [B] Steel > Water > Wood

    Metals are generally excellent conductors of heat due to the presence of free electrons. Non-metals and liquids have lower thermal conductivity. Water's thermal conductivity is higher than most organic materials but significantly lower than metals.

  9. Which one among the following statements about thermal conductivity is correct? [A] Steel > Wood [B] Steel > Water [C] Water > Steel [D] Water > Wood

    Asked in: POST GRADUATE TEACHER (PGT) 2018

    1. Steel > Wood
    2. Steel > Water
    3. Water > Steel
    4. Water > Wood
    Show answer

    Answer: A. Steel > Wood

    Metals like steel are excellent thermal conductors, while materials like wood are poor thermal conductors.

  10. Which of the following gas has the highest thermal conductivity at the same temperature ?

    Asked in: Management Officer (Rajya Sampati Vibhag) Exam 2023

    1. Oxygen
    2. Nitrogen
    3. Hydrogen
    4. Carbon dioxide
    Show answer

    Answer: C. Hydrogen

    Thermal conductivity is a measure of a material's ability to conduct heat. For gases, thermal conductivity is related to the kinetic energy of the molecules and their ability to transfer this energy through collisions. Lighter gases with higher molecular speeds tend to have higher thermal conductivity. Hydrogen molecules are the lightest and move at the highest speeds among the given options, facilitating more efficient heat transfer.