A series circuit contains a 240-$\varOmega$resistor,a 3.8-$\mu$F capacitor,and a 550-mH inductor.It is placed across the terminals of an ac generator with a frequency of f=100 Hz.If the rms current measured in the circuit is 353.5 mA,what is the rms voltage of the generator? A)88.7 V B)250 V C)1.7 * 10⁴ V D)2.25 V E)110 V

Question

Quizplus · Accepted Answer

The rms voltage of the generator can be calculated using the formula for the impedance (Z) in a series RLC circuit and Ohm's law (V = IR). The impedance Z is given by $\sqrt{R^2 + (X_L - X_C)^2}$, where $X_L = 2\pi f L$ is the inductive reactance, $X_C = \frac{1}{2\pi f C}$ is the capacitive reactance, $f$ is the frequency, $L$ is the inductance in henries, and $C$ is the capacitance in farads. Given $R = 240 \Omega$, $L = 550 \times 10^{-3} H$, $C = 3.8 \times 10^{-6} F$, and $f = 100 Hz$, we can calculate $X_L$, $X_C$, and then $Z$. Finally, using $I_{rms} = 353.5 mA$ and $V = IZ$, we find the rms voltage, which matches choice A, 88.7 V.

A Series Circuit Contains a 240- Ω\varOmegaΩ Resistor,a 3 μ\muμ F Capacitor,and a 550-MH Inductor

A Series Circuit Contains a 240- $\varOmega$ Resistor,a 3 $\mu$ F Capacitor,and a 550-MH Inductor