Question

A series circuit consists of a resistance of 4 ohms, an inductance of 500mH and a variable capacitance connected across a 100V,50Hz supply. Calculate the capacitance require to produce a series resonance condition and the voltage generated across both the inductor and the capacitor at the point of resistance.

Answer 1

. At resonance

ωL=1/ωC and I=U/R.

So, we have

C=1/(ω^2 L)=1/((2π∙50)^2∙500∙〖10〗^(-3) )=2.03∙〖10〗^(-5) F.

I=100/4=25 A.

U_L=I∙ωL=25∙2π∙50∙500∙〖10〗^(-3)≈3925 V.

U_C=I∙1/ωC=25∙1/(2π∙50∙2.03∙〖10〗^(-5) )≈3925 V.