According to Joule's Law of Heating, the heat produced (H) in a resistor is directly proportional to the square of the current (I), the resistance (R), and the time (t) for which the current flows: H = I²Rt. Assuming the resistance of the conductor and the time duration are constant, the heat produced is proportional to the square of the current (H ∝ I²). Given that H1 = 2000 J for I1 = 1 A. When the current is doubled, I2 = 2 I1 = 2 A. The new heat produced H2 will be proportional to (I2)²: H2 / H1 = (I2)² / (I1)² H2 / 2000 = (2I1)² / (I1)² H2 / 2000 = 4 (I1)² / (I1)² H2 / 2000 = 4 H2 = 4 2000 J = 8000 J.
A given conductor carrying a current of 1 A produces an amount of heat equal to 2000 J. If the current through the conductor is doubled, the amount of heat produced will be
Asked in UPSC NDA 1 2016 · Topic: Electric Current (Electrical Power and Energy, Joule heating effect)
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