It is known to all of you that the impedance of a circuit is dependent on the frequency of source. In order to study the effect of frequency on the impedance, a student in a lab took 2 impedance boxes `P` and `Q` and connected them 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 `1muF` in series with a resistance of `32 Omega`. And the box `Q` has a coil of self-inductance `4.9 mH` and a resistance of `68 Omega`in series. He adjusted the frequency so that the maximum current flows in `P` and `Q`. Based on his experimental set up and the reading by him at various moment, answer the following questions.
Impedance of box P at the above frequency is

Options

A. `70Omega`
B. `77 Omega`
C. `90 Omega`
D. `100 Omega`

Answer

B

Explanation

`X_C=1/(omegaC)=1/((10^5/7)(10^-6))=70Omega`
`Z_P=sqrt(R_P^2+X_C^(2))`
`=sqrt((32)^+(70)^(2))`
`~~ 77Omega`