Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance 2000 Ω is used to measure the potential difference across 500 Ω resistor, the reading of the voltmeter will be ___________ V.

Solution

Physics sir · 3 steps

A real voltmeter joins the circuit: put its 2000 Ω in parallel with the 500 Ω first, then share the 20 V.

1. Voltmeter in parallel. The voltmeter is connected across the 500 Ω resistor, so its 2000 Ω is in parallel with it. Their combined resistance is (500 × 2000)/(500 + 2000) = 400 Ω.
2. Total current. This 400 Ω is now in series with 600 Ω, giving 1000 Ω in total. The battery current is I = 20/1000 = 0.02 A.

   V = I × R_∥ = 0.02 × 400 = 8 V

3. So. The voltmeter reads the voltage across the parallel combination, which is 8 V.

The common slip: 9.09. Treating the voltmeter as ideal gives 20 × 500/1100 ≈ 9.09 V. The 2000 Ω meter draws current and lowers the reading to 8 V.

The idea to keep. A voltmeter with finite resistance changes the circuit it measures. Combine it in parallel with the element first, then find the voltage.

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