A resistor and capacitor are connected in series with an applied AC voltage source.Separate voltmeter readings across the resistor and capacitor give values of 62 V and 93 V (rms),respectively.What is the effective (rms)voltage of the source?
A) 155 V
B) 145 V
C) 112 V
D) 79 V
E) 158 V

Question

A resistor and capacitor are connected in series with an applied AC voltage source.Separate voltmeter readings across the resistor and capacitor give values of 62 V and 93 V (rms),respectively.What is the effective (rms)voltage of the source?
A) 155 V
B) 145 V
C) 112 V
D) 79 V
E) ​158 V

Quizplus · Accepted Answer

When a resistor and capacitor are connected in series, the voltage drop across the resistor and capacitor must add up to the total voltage of the source. Let's call the voltage of the source V_s. Then we have:

V_s = V_R + V_C

where V_R is the voltage across the resistor and V_C is the voltage across the capacitor.

We are given that V_R = 62 V and V_C = 93 V. Therefore,

V_s = V_R + V_C = 62 V + 93 V = 155 V

This is the effective (rms) voltage of the source. Therefore, the correct choice is C.

A Resistor and Capacitor Are Connected in Series with an Applied