Question

please answer as soon as possible

8. Find (1) Impedance (Z) of circuit and (ii) maximum voltage across capacitor and (ii) rms voltage across inductor. ( 2+2+2). 1 ka 1H V = 140 sin (500 t) HH 1 uF

Answer 1

(i)
Impedance Z for RLC circuit is given by,

Z =  
zex - Tx)+ za


where,
R = Resistance , L = Inductance , C = capacitance, $\omega$ (in rad/s)= 2$\pi$f(in hz)
& X_L = $\omega L$ , X_C= 1/ $\omega C$

Given, R = 1000 $\Omega$
So , Z =
R” + [WL - 1/wC2

=
V10002 + 3141.591-1/13141.59*1 * 10-6}]

= 3296.9 $\Omega$

(ii)

I = V / Z = 140 / 3296.9 = 0.0424 ; I is the current in the circuit , V is the maximum voltage , Z is the impedance
(Maximum Voltage across Capacitor) Vc = I Xc = I * (1/ $\omega C$ ) = 0.0424* ( 1/ 2 pi 50*1*10^-6 ) = 134.96 V

(iii)

VrmsL = Irms * XL = 0.0424 /$\sqrt{2}$ * $\omega L$ =0.03 * 2*pi*500*1 = 94.247 V