A series ac circuit consists of an inductor having a reactance of 80 Ω and an inductance of 190 mH,a 40-Ω resistor,a capacitor whose reactance is 100 Ω,and an ac source.The rms current in the circuit is measured to be 2.2 A.What is the rms voltage of the source?
A) 98 V
B) 96 V
C) 93 V
D) 91 V
E) 88 V

Question

Quizplus · Accepted Answer

The rms voltage of the source can be calculated using the formula $V = IZ$, where $V$ is the rms voltage, $I$ is the rms current, and $Z$ is the impedance of the circuit. The impedance $Z$ of a series RLC circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$, where $R$ is the resistance, $X_L$ is the inductive reactance, and $X_C$ is the capacitive reactance. Substituting the given values, $Z = \sqrt{40^2 + (80 - (-100))^2} = \sqrt{1600 + 180^2} = \sqrt{1600 + 32400} = \sqrt{34000} = 184.39 \Omega$. Therefore, the rms voltage $V = 2.2 A \times 184.39 \Omega = 405.658 V$. However, this calculation seems to have an error in interpretation of the correct answer options provided, indicating a mistake in the calculation process. Correctly calculating, the impedance should be considered with the correct subtraction for reactances, and the final voltage calculation should align with the provided options. Correcting the calculation: $Z = \sqrt{40^2 + (80 - 100)^2} = \sqrt{1600 + 400} = \sqrt{2000} = 44.72 \Omega$. Then, $V = IZ = 2.2 \times 44.72 = 98.384 V$, which rounds to approximately 98 V, matching option A. The initial calculation provided was incorrect; the correct approach gives us the answer as 98 V, aligning with option A.

A Series Ac Circuit Consists of an Inductor Having a Reactance