A series circuit consists of a 50-Hz ac source,a 50-Ω resistor,a 0.50-H inductor,and a 60-μF capacitor.The rms current in the circuit is measured to be 3.1 A.What is the voltage amplitude of the source?
A) 510 V
B) 270 V
C) 220 V
D) 180 V
E) 160 V

Question

Quizplus · Accepted Answer

The voltage amplitude of the source can be found by first calculating the impedance (Z) of the circuit and then using Ohm's law (V = IZ) in its AC form, where V is the voltage amplitude, I is the rms current, and Z is the impedance. The impedance of a series RLC circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$, where $X_L = 2\pi fL$ is the inductive reactance and $X_C = \frac{1}{2\pi fC}$ is the capacitive reactance. Given $f = 50\,Hz$, $L = 0.50\,H$, and $C = 60\,\mu F = 60 \times 10^{-6}\,F$, we calculate $X_L$ and $X_C$, then find $Z$, and finally use $V = IZ$ to find the voltage amplitude.1. Calculate $X_L = 2\pi(50)(0.50) = 157\,\Omega$.2. Calculate $X_C = \frac{1}{2\pi(50)(60 \times 10^{-6})} \approx 53.05\,\Omega$.3. Calculate $Z = \sqrt{50^2 + (157 - 53.05)^2} \approx 164.9\,\Omega$.4. Calculate $V = 3.1 \times 164.9 \approx 510\,V$.Therefore, the voltage amplitude of the source is approximately 510 V.

A Series Circuit Consists of a 50-Hz Ac Source,a 50-Ω