In a Certain Series LCR Circuit

Answer: A. 10.22

In the certain series, LCR circuit resistance R=10.22.

Solution

Power maximum power to occur in series LCR circuit the system should be under resonance,

That means angular frequency ω=1/√LC

So, at ω=1/√LC series LCR circuit will under resonance, and at resonance maximum power will be dissipated in resistor.

Then ω=1/√(10 mH×10 μF)=√10×10³ rad/sec

L=10 mH×√10×10³=10√10

1C=1/10 μF×√10×10³=√10×10

Then impedance Z=√R²+(X_L–X_C)²

At resonance  X_L=X_C

So, impedance Z=R

Maximum current I_max=7√2 A (in LCR circuit maximum current will occur at resonance) 

I_max=V_max/Z

I_max=V_max/R

7√2 A=100 V/R

R=100 V/7√2 A=10.101 ohm.

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