A series ac circuit has voltage supplied to it at a frequency of $25.0 \mathrm { kHz }$ with a phase difference between the current and the voltage of magnitude $0.80 \mathrm { rad }$. If the circuit has a capacitance of $2.0 \mu \mathrm { F }$ and an inductance of $0.030 \mathrm { H }$, find the resistance of the circuit.
A) $0 \mathrm { k } \Omega$
B) $0 \mathrm { k } \Omega$.
C) $0.00 \mathrm { k } \Omega$
D) $4.6 \mathrm { k } \Omega$

Question

Quizplus · Accepted Answer

The resistance in an AC circuit can be found using the phase difference between the current and voltage, along with the values of capacitance and inductance. The phase difference, $\phi$, is related to the reactance and resistance by $\tan(\phi) = \frac{X_L - X_C}{R}$, where $X_L = 2\pi fL$ is the inductive reactance, $X_C = \frac{1}{2\pi fC}$ is the capacitive reactance, and $R$ is the resistance. Given $\phi = 0.80$ rad, $f = 25.0 \times 10^3$ Hz, $C = 2.0 \mu F = 2.0 \times 10^{-6} F$, and $L = 0.030 H$, we can solve for $R$ after calculating $X_L$ and $X_C$. The correct answer involves calculating these values and solving for $R$, which results in a resistance of $4.6 k\Omega$.

A Series Ac Circuit Has Voltage Supplied to It at a Frequency