As shown in the figure, the voltmeter reads 2 V across 5 Ω resistor. The resistance of the voltmeter is _________ Ω.

Solution

Physics sir · 4 steps

The 2 Ω resistor tells you the total current; whatever the 5 Ω does not take must flow through the voltmeter.

1. Read the circuit. The 5 Ω resistor and the voltmeter sit in parallel, and that pair is in series with the 2 Ω resistor across the 3 V cell. The voltmeter reads the voltage across the parallel pair, which is 2 V.
2. Total current. The 2 Ω resistor gets the rest of the cell voltage, 3 - 2 = 1 V. So the main current is I = 1/2 = 0.5 A, and all of it reaches the parallel pair.
3. Split the current. The 5 Ω resistor takes 2/5 = 0.4 A. The voltmeter carries what is left, 0.5 - 0.4 = 0.1 A, with the same 2 V across it.

   R_V = V/I_V = (2 V)/(0.1 A) = 20 Ω

4. So. The voltmeter's resistance is 20 Ω. A real voltmeter draws some current, and here it draws 0.1 A, so it is far from ideal.

The common slip: 4. Stopping at the parallel combination, (2 V)/(0.5 A) = 4 Ω, gives 4. That is the 5 Ω and the voltmeter together, not the voltmeter alone.

The idea to keep. A non-ideal voltmeter is just another resistor in parallel. Find the total current from the series part, subtract what the known resistor takes, and the leftover current gives the meter's resistance.

Answer from the NTA final answer key. Solution by PrepWiser.