Question

AC Circuit in Resonance:

A circuit is constructed with an AC generator, a resistor, capacitor and inductor as The generator voltage varies in time as E Va vb Emsinut, where sm 24 v and w 100 At this frequency, the circuit is in resonance with the maximum value of the current Imax resistance R and the inductance L are unknown. 1) What is L, the value of the inductance of the circuit? mH Submit sin(at) d WW

Answer 1

at resonance :

XL = Xc

XL = w*L

Xc = 1/wC

L = 1/w^2*C

w = 100

L = 0.5435 H = 543.5 mH

part b )

Umax = L*Imax^2/2 =0.11 J

part e )

Imax = Vmax/Z

Z = sqrt(R^2+(XL-Xc)^2)

at resonance XL = Xc

Z = R

R = Vmax/Imax = 24/0.64 = 37.5 ohm

part c )

dU = 1/2 * Imax^2 * RT

T =2pi/w

dU = 0.4825

part d )

Q = 2pi * Umax/dU =1.45