Chapter 26, Problem 81GP

(a) A voltmeter and an ammeter can be connected as shown in Fig. 26–70a to measure a resistance R. If V is the voltmeter reading, and I is the ammeter reading, the value of R will not quite be V/I (as in Ohm’s law) because some of the current actually goes through the voltmeter. Show that the actual value of R is given by

$\frac{1}{R}=\frac{I}{V}-\frac{1}{R_{\text{V}}}.$

where R_V is the voltmeter resistance. Note that R ≈ V/I if R_V ≫ R. (b) A voltmeter and an ammeter can also be connected as shown in Fig. 26–70b to measure a resistance R. Show in this case that

$R=\frac{V}{I}-R_{\text{A}},$

where V and I are the voltmeter and ammeter readings and R_A is the resistance of the ammeter. Note that R ≈ V/I if R_A ≪ R.

FIGURE 26–70 Problem 81.