A box `P` and a coil `Q` are connected in series with an ac source of variable freguency The emf of the source is constant at `28V` The frequency is so adjusted that the maximum current flows in `P` and `Q` Find
(a) impedance of `P` and `Q` at this frequency
(b) voltage across `P` and `Q`
.

Explanation

Current is maximum I e of series resonance
`omega_(r) = (1)/(sqrt(LC)) =(1)/(sqrt( 1.2 xx 10^(-3) xx (25)/(3) xx 10^(-6))) =10^(4) rad//sec`
`X_(C) = (1)/(omega,_(r)C) = (1)/(10^(4) xx (25)/(3) xx 10^(-6)) =12Omega =X_(L)`
`I = (V)/(R_(1) + R_(2)) = (28)/(16 + 12) =(28)/(28) =1A`
`Z_(p) = sqrt((16)^(2) + (X_(L))^(2)) = sqrt((16)^(2) + (12)^(2)) =20Omega`
`Z_(Q) = sqrt((12)^(2) + (X_(L)^(2)) = sqrt((12)^(2) + (12)^(2))) =12sqrt2Omega`
`V_(P) = iZ_(p) = 1xx 20 =20V`
`V_(Q) = iZa = 1 xx 12 sqrt2 = 12sqrt2V` .