Halliday, Resnick & Walker — Circuits: Problem 38

38 In Fig. 27-42, a voltmeter of resistance \( R_V = 300 \, \Omega \) and an ammeter of resistance \( R_A = 3.00 \, \Omega \) are being used to measure a resistance \( R \) in a circuit that also contains a resistance \( R_0 = 100 \, \Omega \) and an ideal battery of emf \( \mathcal{E} = 28.5 \, \text{V} \). Resistance \( R \) is given by \( R = V/i \), where \( V \) is the voltmeter reading and \( i \) is the current in resistance \( R \). However, the ammeter reading is not \( i \) but rather \( i' \), which is \( i \) plus the current through the voltmeter. Thus, the ratio of the two meter readings is not \( R \) but only an apparent resistance \( R' = V/i' \). If \( R = 85.0 \, \Omega \), what are (a) the ammeter reading, (b) the voltmeter reading, and (c) \( R' \)? (d) If \( R_V \) is increased, does the difference between \( R' \) and \( R \) increase, decrease, or remain the same?