Question

A RLC circuit is driven by an AC source of 120volts with frequency 60H_z. The resistance is 2000 Ohm, the capacitance is 500 mu F, and the inductance is 100_m M. Find the inductive reactance, The capacitive reactance, the impedance, the current, and the resonant frequency.

Answer 1

inductive reactance = $\omega L$

= 2 x 3.14 x 60 x 100x 10^-3

   ^{= 37.68}

capacitive reactance = $\frac{1}{\omega C}$

= 1/ 2 x 3.14 x 60 x 500x 10^-6

   ^{= 5.30}

Impedence = $Z = \sqrt{R^{2}+(X_{c}- X_{L})^{2}}$

   = $Z = \sqrt{2000^{2}+(1048.5)}$

   =2000.26

$\omega L = \frac{1}{\omega C}$

$f = \frac{1}{2\Pi \sqrt{LC}}$ \

   = 1 / 2 x 3.14 x 7.07 x 10^-3

  ^{= 22.52 hz}