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Question

A resistor of resistance R, capacitor of capacitance C and inductor of inductance L are connected in parallel to AC power source of voltage ϵ0sinωt. The maximum current through the resistance is half of the maximum current through the power source. Then value of R is

A
3ωC1ωL
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B
31ωCωL
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C
51ωCωL
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D
None of these
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Solution

The correct option is A 3ωC1ωL
The phasor diagram for the situation is shown in figure.

iR0(iR0)2+(ϵ0ωCϵ0ωL)2=12
or,
iR0(iR0)2+(iC0iL0)2=12 0R(0R)2+(0ωC0ωL)2=12
R=3ωC1ωL

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