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 `1 mu F` in series with a resistance of `32 Omega`. Coil `Q` has a self-inductance 4.9 mH and a resistance of `68 Omega` in series. The frequency is adjusted to that the maximum current flows in `P` and `Q`. At this frequency
(a) The impedance of `P` is `77 Omega`
(b) The impedance of `Q` is `85 Omega`
(c ) Voltage across `P` is `7.7 V`
(d) Voltage across `Q` is `9.7 V`

Options

A. Only (a),(c ) are correct
B. Only (a),(d) are correctd
C. Only (c ), (d) are correct
D. (a),(c ),(d) are correct

Answer

D

Explanation

`i_(0) = (V_(0))/(R ) , Z_(p) = sqrt(R_(1)^(2) + X_(c )^(2)) , Z_(Q) = sqrt(R_(2)^(2) + X_(L)^(2))`
`V_(P) = i_(0) Z_(p)` and `V_(Q) = i_(0) Z_(Q)`