Question

Two equal resistors of 15 kΩ each are connected in series across a 120 V source. A voltmeter when connected across each read 48 V in each case. Determine the resistance of the voltmeter.

Answer 1

$$R_{eq}=\frac{15*R}{15+R}+15$$

$$I=\frac{V}{R_{eq}}=\frac{120}{\frac{15*R}{15+R}+15}$$

$$V_{ab}=120-I*15$$

$$48=120-\frac{120}{\frac{15*R}{15+R}+15}=120(1-\frac{15+R}{30R+225})$$

$$\frac{15+R}{30R+225}=0.6$$

$$18R-135=15+R$$

$$R=8.8\:\Omega$$