In a series LCR circuit `R= 200(Omega)` and the voltage and the frequency of the main supply is 220V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by `30(@)`. On taking out the inductor from the circuit the current leads the voltage by `30(@)`. The power dissipated in the LCR circuit is

Options

A. `210 W`
B. `Zero W`
C. `242 W`
D. `305 W`

Answer

C

Explanation

Here, `R = 200 Omega, E_(upsilon) = 220 V, v = 5.0 Hz`
In `L -R` circuit Fig. `tan 30^(@) = (X_(L))/(R )`
In `C - R` circuit Fig., `tan 30^(@) = (X_(C ))/(R )`
`:. (X_(L))/(R ) = (X_(C ))/(R )` or `X_(L) = X_(C )`.
In `LCR` circuit, if `theta` is the phase difference between voltage and current, then
`tan theta = (X_(L) =X_(C ))/(R ) = (0)/(200) = 0` or `theta = 0^(@)`
i.e., current and voltage are in the same phase.
`:.` Average power `E_(upsilon) I_(upsilon) cos theta`
`= (E_(upsilon)^(2))/(R ) cos 0^(@) = ((220)^(2))/(220) = 242 W`