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RLC Circuits and Resonance - Technical MCQs

Q1:

What is the voltage across R1, C1, and L1?

A VR = 156 V, VC = 165 V, VL = 441 V

B VR = 178 V, VC = 187 V, VL = 503 V

C VR = 219 V, VC = 232 V, VL = 619 V

D VR = 260 V, VC = 276 V, VL = 735 V

ANS:A - VR = 156 V, VC = 165 V, VL = 441 V

If you need to understand the solution check below.

Xl=(2.pi.f.L) => 2*3.14*1500*3 => 28,274ohm.
Xc= ( 1/2.pi.f.C) => 1/2*3.14*1500*0.01uF => 10,610ohm.

Vt=317v ( total).
Vr=I*R ( resis).
Vl=I*Xl (Induc).
Vc=I*Xc (caps).

(Note Vl and Vc are in reverse angle). So Vl - Vc in one vertical plane. Vr is horizontal.

I is same in all the devices but V is not same in degree so use Pythagoras, then we get,

sqr(Vt) = sqr(Vr) + sqr(Vl - Vc).
sqr(317) = sqr(I*R) + sqr(I*Xl - I*Xc).
sqr(317) = sqr(I) *( sqr(10K) + sqr(28,274 - 10,610) ).

sqr(I)= sqr(317)/ sqr(10K) + sqr(17,664).

I = sqrt(2.43895- e4).
I = 0.015617A.
= 15.617mA.

Vr = I*R = 0.015617*10k = 156V.
Vl = I*Xl = 0.015617 * 28,274 = 441V.
Vc = I*XC = 0.15617 * 10,610 = 165V.