A `100 V` a.c. source of frequency `50 Hz` is connected to a `LCR` circuit with `L = 8.1` millihenry, `C = 12.5 mu F` and `R = 10` ohm, all connected in series. What is the potential difference across the resistance?

Options

A. `100 V`
B. `200 V`
C. `300 V`
D. `450 V`

Answer

1

Explanation

Here, `E_(V) = 100 V, v = 500 Hz`
`L = 8.1 xx 10^(-3) H, C = 12.5 xx 10^(-6) F, R = 10 Omega`
`X_(L) = omega L = 2 pi v L = 1000 pi xx 8.1 xx 10^(-3) = 25.4 Omega`
`X_(C ) = (1)/(omega C) = (1)/(1000 pi xx 12.5xx 10^(-6))`
`= (10^(3))/(12.5 pi) Omega = 25.4 Omega`
`Z = sqrt(R^(2) + (X_(L) - X_(C ))^(2))`
`=sqrt(10^(2) + (25.4 - 25.4)^(2)) = 10 Omega`
`I_(v) = (E_(v))/(Z) = (100)/(10) = 10 A`
Potentail difference across `R = I_(v) R`
`= 10 x 10 = 100 V`