Question

A high-impedance ac voltmeter is connected in turn across the inductor, the capacitor, and the resistance in a series circuit having an ac source of 100 V(rms) and gives the same reading in volts in each case. Then, this reading is:

• A. 100/3 volts
• B. 300 volts
• C. 100 volts
• D. incomplete data

Answer 1

Answer: (C)

100 volts

Let the same reading be $xV$,
then let, $Z_{total}=R+j(X_L-X_C)=Z\angle \theta I=\frac{V_S}{Z}\angle -\theta therefore,V_R=|\frac{V_S}{Z}R\angle -\theta |V_L=|\frac{V_S}{Z}{X}_L\angle 90-\theta |V_C=|\frac{V_S}{Z}{X}_C\angle -90-\theta |given,V_R=V_L=V_V=x\Rightarrow R=X_L=X_C\Rightarrow Z_{total}=R=Z\angle 0=Z\Rightarrow V_R=|\frac{V_S}{Z}R\angle -\theta |=V_S{V}_L=|\frac{V_S}{Z}{X}_L\angle 90-\theta |=\left|j{V}_S\right|=V_S{V}_C=|\frac{V_S}{Z}{X}_C\angle -90-\theta |=|-j{V}_S|=V_S\Rightarrow x=V_S=100V$