Impedance: A 25.0-mH inductor, a 2.00-μF capacitor, and a certain resistor are connected in series across an ac voltage source at 1000 Hz. If the impedance of this circuit is 200 Ω, what is the resistance of the resistor?

Question

Quizplus · Accepted Answer

The impedance of the circuit is given by:
$$Z=\sqrt{R^2+(X_L-X_C)^2}$$
where $R$ is the resistance, $X_L=2\pi f L$ is the inductive reactance, and $X_C=1/(2\pi f C)$ is the capacitive reactance. Substituting the given values, we get:
$$200=\sqrt{R^2+\left(2\pi(1000)(0.025)-\frac{1}{2\pi(1000)(2	imes10^{-6})}ight)^2}$$
Solving for $R$, we get:
$$R=184\ \Omega$$
Therefore, the answer is B.

Impedance: a 25