Question

The circuit depicted in the figure is employed for studying Ohm’s Law. Instead of using a standard resistor, a student opts for a glass tube filled with mercury (tube 1), connected to the circuit through two electrodes, E1 and E2. He records the readings of the ammeter and voltmeter, thereby calculating the resistance. The student repeats the experiment by substituting tube 1 with tube 2, where the same amount of mercury fills tube 2.

Neglecting internal resistance of the cell use (> or < or =) to compare:

1. the resistance in both the cases.
2. the voltmeter readings in both the cases.
3. the specific resistance in both the cases.

Answer 1

1. The resistance of tube 2 is less than the resistance of tube 1 because resistance depends directly on the length and inversely on the area of the resistor, and tube 2 is thicker and shorter than tube 1.
2. The voltmeter reading for tube 1 is the same as the voltmeter reading for tube 2 because, according to Ohm’s law, the potential difference across a resistor depends only on the current applied, not on the resistance of the resistor.
3. As the specific resistance of a resistor is independent of its dimensions but depends only on the contained material, and since here both tubes contain only mercury, the specific resistance in both cases is the same.