Calculate L for a solenoid which has 120 volt induced voltage when current throu

Question

Calculate L for a solenoid which has 120 volt induced voltage when current through it is changing at 1200 A/s. Calculate resonance frequency of a series RLC circuit.if above solenoid is used with C = 1 microfarad. If R is 100 ohms.what is the Q-factor? Calculate total impedance of the circuit at 100 rad/sec.1000 rad/sec and at 10. 000 rad/sec. If the voltage amplitude for AC voltage is Vo = 12 volt.what would be the current amplitude lo at 1000 rad/sec. Calculate the Power amplitude Po at 1000 rad/sec.

Explanation / Answer

V=L(di/dt)

Or, 120=L(1200)

So, L=0.1H

For series resonance, angular frequency=w=1/((LC)^0.5)=1/((0.1*1*10^-6)^0.5)=3162.27/s

Q factor=wL/R=3162.27*0.1/100=3.16

Impedance is Z=(R^2 + (wL-(1/wC))^2)^0.5

Putting values of w as 100,1000 and 10000 for given cases, the impedance obtained are Z = 9990.5, 905.53 and 905.53 for the given frequencies.

At 1000/s frequency, Current amplitude I = V/Z = 12/905.53 = 0.0132A

At 1000/s, Power amplitude = current amplitude * voltage amplitude = 0.1584W

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