The experimental setup in Fig. 5 below measures the value of unknown resistance in two steps : * When $V = 24$ V, $r$ is set at $400 \Omega$ and $S = 80 \Omega$, the galvanometer shows a deflection of $30^{\circ}$. * When switch is thrown to position 2, the supply voltage drops down to $12$ V and the galvanometer still shows a deflection of $30^{\circ}$. The value of unknown resistance is

The problem describes an experimental setup for measuring an unknown resistance using a galvanometer. It provides two scenarios with different supply voltages ($V$) and resistance settings ($r$ and $S$), where the galvanometer shows the same deflection ($30^{\circ}$) in both cases. This suggests that the current through the galvanometer, or some quantity proportional to it, remains constant. In resistance measurement experiments like the Wheatstone bridge, the galvanometer is typically used to indicate a balanced condition (null deflection) or a specific level of imbalance. The fact that the voltage is halved while the deflection remains the same implies a specific relationship between the resistances in the circuit. Without the diagram of the experimental setup, a precise derivation is impossible. However, problems of this nature in physics often relate to the principle of ratios in bridges or potentiometers. The answer being one of the given options suggests a unique solution exists for a particular circuit configuration.