Answer to Question #135399 in Electric Circuits for akku

Question

1. A series RLC circuit containing a resistance of 25Ω, an inductance of 0.22H and a capacitor
of 80uF are connected in series across a 220V, 50Hz supply. Calculate the total circuit
impedance, the circuits current, power factor and draw the voltage phasor diagram.

Answer 1

As per question

L=0.22H

R=25$\Omega$

C=80$\mu f$

frequency $f=50hz$

Voltage V=$220 volts$

Inductive reactance $X_L=\omega L=2\pi fL$

=$2\times 3.14\times 50\times 0.22$

=$69.08\Omega$

Capacitive Reactance $X_c=\frac{1}{\omega C}=\frac{1}{2\pi f C}$

=$\frac{10^6}{2\times 3.14\times 50 \times 80}$

=$39.8\Omega$

Here $X_L>X_c$

$X_L-X_c=29.27\Omega$

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

$=\sqrt{25^2+29.27^2}$

=$\sqrt{1481.79}$

=38.49$\Omega$

Current =$\frac{voltage}{impedance}=\frac{V}{Z}$

=$\frac{220}{38.49}$

=5.7 A

Power factor=$\frac{R}{Z}$

=$\frac{25}{38.49}$

=0.5715

Voltage Phasor is given by,