Question

A series RCL circut in which R=1.50e3 ohms and C= 15.0e-9 F is conneceted to a generator whose frequency is variable. When the frequency is adjusted to 50.5 kHz, the rms current reaches a maximum of 0.140 A. What is the inductance of the inductor? The rms voltage of the generator? The phase angle between emf and current? The power output of the generator?

Answer 1

given that R=1.5*10^3 ohms

C=15*10^(-9) F

part a :

current will be maximum ,when the frequency is equal to resonant frequency

resonant frequency=1/(2*pi*sqrt(L*C))

==>50.5*1000=1/(2*pi*sqrt(L*15*10^(-9))

==>L=1/((2*pi*50.5*1000)^2*15*10^(-9))=0.66217 mH

part b:

rms voltage of the generator=maximum value of rms current*resistance (as at the time of resonance, total impedance in the circuit=resistance)

=0.14*1.5*10^3=210 volts

part c:

as net impedance is equal to resistance and the system is in resonance, phase angle between emf and current is 0 degrees

part d:

power output=rms voltage*rms current

=210*0.14=29.4 W