Chapter 24, Problem 3Q

1. (a) Prove that the true resistance R is given by

   $R=R^{\prime }\left(1-\frac{R_{\text{a}}}{R^{\prime }}\right)$

   where R′ = V/I is the measured resistance as given by the voltmeter and ammeter readings for measurements done by the arrangement in Fig. 24.2 or Fig. 24.5b. Is the true resistance larger or smaller than the apparent resistance?

2. (b) Prove that the true resistance R is given approximately by

   $R=R^{\prime }\left(1+\frac{R^{\prime }}{R_{\text{v}}}\right)$

3. 1. where R′ = V/I is the measured resistance as given by the voltmeter and ammeter readings for measurements done by the arrangement in Fig. 24.1 or Fig. 24.5a. (Hint: Use the binomial theorem.)

   $\frac{1}{1-\frac{R^{\prime }}{R_{\text{v}}}}\simeq 1+\frac{R^{\prime }}{R_{\text{v}}}$

   Is the true resistance larger or smaller than the apparent resistance? Explain.