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Solved Problems-9

In the circuit shown in figure, find out the value of R such that the impedance of the whole circuit should be independent of the frequency of the supply. If voltage = 200 V, L = 0.16 H and C = 100 μF, calculate the power loss in the circuit.
Description: 1564.png
Impedance of the inductive branch, ZL = (R + jωL)
Impedance of the capacitive branch, Description: 3677.png
∴ Impedance of the whole circuit,
Description: 3683.png
In this expression, the imaginary term of the numerator is R times the imaginary term of the denominator. Thus, if the real term i.e., Description: 3689.png is also R times the real term of the denominator i.e. R × 2R, then the term consisting of w will vanish and the impedance will become independent of frequency.
Thus, the condition is,
Description: 3695.png
Putting the value of L and CDescription: 3701.png
Power loss in the circuit, Description: 3707.png

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