A $120 - \mathrm { V }$ rms voltage at $60 \mathrm {~Hz}$ is applied across an $R C$ circuit. The rms value of the current in the circuit is $0.60 \mathrm {~A}$, and it leads the voltage by $60 ^ { \circ }$. What is the resistance in this circuit?
A) $100 \Omega$
B) $120 \Omega$
C) $200 \Omega$
D) $60 \Omega$
E) $150 \Omega$

Question

Quizplus · Accepted Answer

The resistance $R$ in the circuit can be found using Ohm's Law, $V = I \cdot Z$, where $V$ is the voltage, $I$ is the current, and $Z$ is the impedance. Given that the current leads the voltage by $60^\circ$, this indicates that the phase angle $\theta = 60^\circ$, which is typical for an $RC$ circuit where the impedance $Z$ has both resistive ($R$) and capacitive ($X_C$) components. The phase angle $\theta$ in an $RC$ circuit is given by $\tan^{-1}(X_C/R)$, but more directly relevant here is the calculation of resistance using the given information.The power factor (cos$\theta$) in this case is $\cos(60^\circ) = 0.5$, and the impedance $Z$ can be calculated as $V/I$. Given $V = 120V$ (rms) and $I = 0.60A$ (rms), $Z = 120V / 0.60A = 200\Omega$. However, the actual resistance $R$ can be found by considering the power factor, which is the ratio of the resistance $R$ to the impedance $Z$. Since the power factor is equal to $R/Z$, and we know the power factor is $0.5$, we can solve for $R$ as follows:$$R = Z \cdot \cos(\theta) = 200\Omega \cdot 0.5 = 100\Omega$$Therefore, the resistance in the circuit is $100\Omega$.

A 120−V120 - \mathrm { V }120−V Rms Voltage At 60 Hz60 \mathrm {~Hz}60 Hz

A $120 - \mathrm { V }$ Rms Voltage At $60 \mathrm {~Hz}$