Q.

An A.C. circuit contains a resistor 'R', an inductor 'L' and a capacitor 'C' connected in series. When it is connected to an A.C. generator of fixed  output voltage and variable frequency, the current in the circuit is found to be leading the applied voltage π / 4 rad, when the frequency is f1. When the frequency of the generator increased to 'f2' the current is found to be lagging behind the applied voltage by π / 4 rad. The
resonant frequency of the circuit is 

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a

f1f2

b

f1f2f1+f2

c

2f1f2f1+f2

d

f1+f22

answer is D.

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Detailed Solution

1= 2πf1L-12πf1CR 1= 12πf2C-2πf2LR 2πL(f1+f2)=12πC1f1+1f2 4π2LC=1f1f2 Resonant frequency= f1f2

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