What is the resonant impedance of a series RLC circuit with a 15 mH inductor, 0.015$\mu \mathrm { F }$ capacitor and 80$\Omega$ resistor?
A) 30 $\Omega$
B) 15 $\mathrm { k } \Omega$
C) 80$\Omega$
D) 0 $\Omega$

Question

What is the resonant impedance of a series RLC circuit with a  15 mH  inductor,  0.015$\mu \mathrm { F }$  capacitor and  80$\Omega$ resistor?
A)  30 $\Omega$
B) 15 $\mathrm { k } \Omega$
C)  80$\Omega$ 
D) 0 $\Omega$

Quizplus · Accepted Answer

The resonant frequency of a series RLC circuit is given by:
$$f = \frac{1}{2\pi\sqrt{LC}}$$

We can calculate the resonant frequency using the given values:
$$f = \frac{1}{2\pi\sqrt{(15\times10^{-3})(0.015\times10^{-6})}} \approx 1414\mathrm{Hz}$$

The impedance of a series RLC circuit at resonance is given by:
$$Z_R = R$$

Therefore, the resonant impedance of the given circuit is 80$\Omega$. Thus, the correct choice is C).

What Is the Resonant Impedance of a Series RLC Circuit μF\mu \mathrm { F }μF

What Is the Resonant Impedance of a Series RLC Circuit $\mu \mathrm { F }$