The power factor of an ac $R L$ circuit with a $100 - \Omega$ resistor and a certain inductor is $0.60$. What is the impedance of the circuit?
A) $100 \Omega$
B) $170 \Omega$
C) $85 \Omega$
D) $340 \Omega$
E) $60 \Omega$

Question

Quizplus · Accepted Answer

The power factor of an AC circuit is defined as the cosine of the phase angle ($\theta$) between the voltage and current. For an $RL$ circuit, the power factor is given by $\cos(\theta) = \frac{R}{Z}$, where $R$ is the resistance and $Z$ is the impedance. Given the power factor is $0.60$, and $R = 100 \Omega$, we can solve for $Z$ as follows: $0.60 = \frac{100}{Z}$, which gives $Z = \frac{100}{0.60} = 166.67 \Omega$, which is approximately $170 \Omega$.

The Power Factor of an Ac RLR LRL Circuit with A 100−Ω100 - \Omega100−Ω

The Power Factor of an Ac $R L$ Circuit with A $100 - \Omega$