Question

A RLC circuit resonates at 5000 Hz it has an inductor with a DC resistance of 65 ohms, a 0.47 F capacitor and a 330 ohm resistor. What is the value of the inductor?

What would be the impedance of the circuit at 2400Hz?

What is the expected phase angle between the input voltage and the current at 2400 Hz?

NEED ANSWERS FOR ALL 3 SINCE THEY ARE CONNECTED TO EACH OTHER. PLEASE AND THANK YOU!

Answer 1

We know that

The resonant frequency isgiven by

w =Sqrt(1/LC)

Then the inductor L is =1/w²C =1/(2*3.14*5000)²*0.47=2.157nH

b)

When the frequency f =2400Hz then the

Capacitive reactance is Xc =1/wC =1/2pifC =1/2*3.14*2400*0.47 =141.16micro-ohm

Inductative reactance is XL =wL =(2*pif)L =2*3.14*2400*2.157nH=32.5micro-ohm

Now the impedance Z =Sqrt(R²+(XL-Xc)² =Sqrt( (65+330)2 +(108.66)2=409.673ohm

now the phase angle is

@ =tan^-1(XL-Xc/R)=tan^-1(32.5-141.16/409.673) =14.854degrees