Question

Calculate the impedance (magnitude, phase angle) of a RLC series circuit (R = 1 k Ohm, C = 2 muF, L = 1 H) at frequency f= 2500 Hz.

Answer 1

Explanation:

It is given that,

Resistance, $R=1\ k\Omega=10^3\ \Omega$

Capacitance, $C=2\ \mu F=2\times 10^{-6}\ F$

Inductance, L = 1 H

Frequency, f = 2500 hz

We need to find the impedance of the circuit. It is given by :

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

Where, $X_L=2\pi fL$ is inductive reactance

$X_C=\dfrac{1}{2\pi f C}$ is capacitive reactance

$Z=\sqrt{R^2+(2\pi fL-\dfrac{1}{2\pi f C})^2}$

$Z=\sqrt{(10^3)^2+(2\pi \times 2500\times 1-\dfrac{1}{2\pi \times 2500\times 2\times 10^{-6}})^{2}}$

Z = 15707.99 ohms

Phase angle is given by :

$\phi=tan^{-1}(\dfrac{X_L-X_C}{R})$

$\phi=tan^{-1}(\dfrac{2\pi \times 2500\times 1-\dfrac{1}{2\pi \times 2500\times 2\times 10^{-6}}}{10^3})$

$\phi=86.34$

Hence, this is the required solution.