Question

A resistance R is connected to a voltage source V having internal resistance RI. A voltmeter of resistance R2 is used to measure the voltage across R. The reading of the voltmeter is _____________

(a) \(\frac{V_S R_1 R_2}{R_2 R_1 + R_1 R + RR_2}\)

(b) \(\frac{V_s R}{R + R_s}\)

(c) \(\frac{VR_1 R_2}{R_1 R_2 – R_1 R – RR_2}\)

(d) \(\frac{V_S RR_2}{R_1 R_2 + R_1 R + RR_2}\)

I had been asked this question in an international level competition.

Question is taken from Advanced Problems on Network Theory in chapter Network Theory and Complex Circuit Diagram of Network Theory

Answer 1

Right choice is (d) \(\frac{V_S RR_2}{R_1 R_2 + R_1 R + RR_2}\)

Explanation: Effective resistance of R and Rm is

Req = \(\frac{RR_m}{R + R_m}\)

Therefore the reading is \(\frac{V}{R_1 + \frac{R}{R + R_2}}\Big[\frac{RR_2}{R+R_2}\Big]\)

= \(\frac{V_S RR_2}{R_1 R_2 + R_1 R + RR_2}\).