# LRC Series AC Circuit – problems and solutions

1.

Determine the electric current in circuit (1 µF = 10^{-6} F)

__Known :__

Resistor (R) = 12 Ohm

Inductor (L) = 0.075 H

Capacitor (C) = 500 µF = 500 x 10^{-6} F = 5 x 10^{-4} Farad

Voltage (V) = V_{o} sin ωt = v_{o} sin 2πft = 26 sin 200t

__Wanted :__ Electric current

__Solution :__

__Impedance (Z) :__

*The inductive reactance (X*_{L}*) = **ωL = (200)(0,075) = 15 Ohm*

*The capacitive reactance (X*

_{C}

*) = 1 / ωC = 1 / (200)(5 x 10*

^{-4}

*) = 1 / (1000 x 10*

^{-4}

*) = 1 / 10*

^{-1}

*= 10*

^{1}

*= 10 Ohm*

*Resistor (R) = 12 Ohm*

__Electric current (I)__ :

I = V / Z = 26 Volt / 13 Ohm

I = 2 Volt/Ohm

I = 2 Amp

2. If the impedance of the circuit is 250 Ω, determine resistance of resistor R.

__Known :__

The impedance of the circuit (Z) = 250 Ω

Capacitor (C) = 8 m F = 8 x 10^{-6} F

Inductor (L) = 0.8 H

Voltage (V) = 200 Volt

w = 500 rad/s

__Wanted :__ Resistance of resistor (R)

__Solution :__

3. Determine the potential difference of both edge of the inductor.

__Known :__

R = 40 W

X_{L }= 150 W

X_{C}= 120 W

V = 100 Volt

__Wanted:__ the potential difference

__Solution :__

The total impedance Z of the circuit :

The potential difference of both edge of the inductor :