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 23 V and 29 V (rms),respectively.What is the effective (rms)voltage of the source?
A)7.2 V
B)47 V
C)37 V
D)26 V
E)18 V

Question

Quizplus · Accepted Answer

We know that the voltage across a resistor (Vr) and a capacitor (Vc) in series with an AC voltage source are given by:

Vr = IR × R          and         Vc = IC × XC

where IR and IC are the currents flowing through the resistor and capacitor, and R and XC are the resistance and reactance of the resistor and capacitor respectively.

Since the resistor and capacitor are in series, the current flowing through them must be the same. Hence, we can write:

IR = IC = I        (let's call it I)

We also know that the voltage across the source (Vs) is the phasor sum of the voltage across the resistor and the voltage across the capacitor, i.e.,

Vs = √(Vr^2 + Vc^2)

Substituting the given values, we get:

Vs = √(23^2 + 29^2) = √(529 + 841) = √1370 = 37.01 V (approx.)

Therefore, the effective (rms) voltage of the source is 37 V.

A Resistor and Capacitor Are Connected in Series with an Applied