A circuit consists of a noniductive resistor of `50 Omega`, a coil of inductance `0.3 H` and resistance `2 Omega`, and a capacitor of `40 mu F` in series and is supplied with 200 volt rms at 50 cycles `//` sec. Then

Options

A. the current lag or lead by an angle `15^(@) 5^(1)`
B. the power in the circuit is `710.4 W`
C. the power in th circuit is `640 W`
D. the current lag or lead by an angle `12^(@) 5^(1)`

Answer

A,B

Explanation

Total resistance `R = 50 + 2 = 52 Omega`
`L = 0.3 H, C = 40 xx 10^(-6) F`
`Z = sqrt(R^(2) + (X_(L) - X_(C ))^(2))` ,
`X_(L) = omega L = 2 xx pi xx 50 xx 0.3 = 30 pi`
`X_(c ) = (1)/(omega C) = (1)/(2 xx pi xx 50 xx 40 xx 10^(-6)) = 250 pi`
`X_(c ) gt X_(L)` so current leads the applied voltage.
`Z = sqrt(R^(2) + (X_(L) - X_(C ))^(2)) = sqrt((52)^(2) + (30 pi - 250 pi)^(2))`
`I_("rms") = (V_("rms"))/(2)`
`P_(av) = E_("rms") I_("rms") cos phi = E_("rms") E_("rms")/(2) xx (R )/(2) = (E_("rms")^(2) R)/(2)`