Question

A parallel resonant circuit has a capacitor 100pF in one branch and the impedance of 100 micro Henry plus a a resistance of 10 ohms in another parallel branch, calculate:

(a) resonant frequency

(b) impendance of the circuit at the resonance and the line current at resonance

(c) Q-quality factor of the circuit

Answer 1

Resources frequency

$f_r=\frac{1}{2\pi\sqrt{LC}}$

$f_r=\frac{1}{2\pi\sqrt{100\times10^{-12}\times100\times10^{-6}}}$

$f_r=1.6$ Hz

Impedance

$Z=\sqrt{R^2+({X_L-X_c})^2}$

$$Z=\sqrt{10^2+({2\pi\times1.6\times100\times10^{-6}-\frac{1}{2\pi\times1.6\times100\times10^{-12}}})^2}$$

$$Z=\sqrt{990466.24+100}=\sqrt{990566.2424}=995\Omega$$

C.

$Q=\frac{w_rL}{R}=\frac{10^7\times100\times10^{-6}}{10}=100$