The phase angle of an $R L C$ series ac circuit with an inductive reactance of $200 \Omega$ and a capacitive reactance of $100 \Omega$ is $40.0 ^ { \circ }$. What is the resistance of the resistor in this circuit?
A) $200 \Omega$
B) $100 \Omega$
C) $119 \Omega$
D) $156 \Omega$
E) $265 \Omega$

Question

Quizplus · Accepted Answer

The phase angle $\theta$ in an RLC series circuit is given by $\tan(\theta) = \frac{X_L - X_C}{R}$, where $X_L$ is the inductive reactance, $X_C$ is the capacitive reactance, and $R$ is the resistance. Given $X_L = 200 \Omega$, $X_C = 100 \Omega$, and $\theta = 40^\circ$, we can solve for $R$. Rearranging the formula gives $R = \frac{X_L - X_C}{\tan(\theta)}$. Substituting the given values, $R = \frac{200 \Omega - 100 \Omega}{\tan(40^\circ)} \approx 119 \Omega$.

The Phase Angle of An RLCR L CRLC Series Ac Circuit with an Inductive Reactance Of

The Phase Angle of An $R L C$ Series Ac Circuit with an Inductive Reactance Of