A box P and a coil Q are connected in series with an ac source of variable frequency. The emf of the source is constant at 10 V. Box P contains a capacitance of `32 Omega`. Coil Q has a self inductance of 4.9 mH and a resistance of `68 Omega` in series. The frequency is adjusted so that maximum current flows in P and Q.

The impedance of P at this frequency is

Options

A. `77 Omega`
B. `36 Omega`
C. `40 Omega`
D. `125 Omega`

Answer

A

Explanation

As this circuit is a series LCR circuit, cuttent will be maximum at reasonance , i.e.
`omega = (1)/(sqrt(LC))v =(1)/(sqrt((4.9 xx10^(-3))(10^(-6)))=(10^5)/(7) rad s^(-1)`
with `I=(V)/(R ) =(10)/((32+68))=(1)/(10)A`
so the impedance, `Z_(P)=[R_(1)^(2)+(1//omegaC)^(2)]^(1//2) = sqrt(5924)=77 Omega`.