A 100 v resistor,a 20 mH inductor and a capacitor are connected in series with a time varying emf of 10.0 V and frequency 1000 Hz.The impedance of the circuit is 339 $\varOmega$ .What is the capacitance of the capacitor?
A)0.354 µF
B)3.0 µF
C)0.153 µF
D)0.289 µF

Question

Quizplus · Accepted Answer

The impedance $ Z $ of an RLC series circuit is given by $ Z = \sqrt{R^2 + (X_L - X_C)^2} $, where $ X_L = 2\pi f L $ and $ X_C = \frac{1}{2\pi f C} $. Given $ Z = 339 \, \Omega $, $ R = 100 \, \Omega $, $ L = 20 \, \text{mH} $, and $ f = 1000 \, \text{Hz} $, solve for $ C $ using the formula. The correct capacitance is approximately 0.354 µF.

A 100 V Resistor,a 20 MH Inductor and a Capacitor Ω\varOmegaΩ

A 100 V Resistor,a 20 MH Inductor and a Capacitor $\varOmega$