A series RLC circuit with L = 5 H,C = 10 µF,and R = 10 $\Omega$ is driven by a generator with a maximum EMF of 100 V and a variable frequency.The resonant frequency f₀ of this circuit is A)22.5 Hz B)45.0 Hz C)90.0 Hz D)180 Hz E)360 Hz

Question

Quizplus · Accepted Answer

The resonant frequency of a series RLC circuit is given by:$$f_0 = \frac{1}{2\pi\sqrt{LC}}$$Substituting the given values:$$f_0 = \frac{1}{2\pi\sqrt{(5 H)(10 \mu F)}}$$$$f_0 = \frac{1}{2\pi\sqrt{50 	imes 10^{-6}}}$$$$f_0 = \frac{1}{2\pi\sqrt{0.0005}}$$$$f_0 = \frac{1}{2\pi(0.0224)}$$$$f_0 = 22.5 Hz$$Therefore, the resonant frequency of the circuit is 22.5 Hz.

A Series RLC Circuit with L = 5 H,C = Ω\OmegaΩ

A Series RLC Circuit with L = 5 H,C = $\Omega$