A `0.2 k Omega` resistor and `15 mu F` capacitor are connected in series to a 220 V, 50 Hz ac source. The impedance of the circuit is

Options

A. `250 Omega`
B. `268 Omega`
C. `29.15 Omega`
D. `291.5 Omega`

Answer

D

Explanation

Here, `R=0.2 k Omega = 200 Omega`
`C =15 mu F = 15xx10^(-6)F, V_("rms")=220 V, upsilon = 50 Hz`
Capacitive reactance,
`X_(C )=(1)/(2pi upsilon C)=(1)/(2xx3.14xx50xx15xx10^(-6))=212 Omega`
The impedance of the Rccircuit is
`Z = sqrt(R^(2)+X_(C )^(2))=sqrt((200)^(2)+(212)^(2))=291.5 Omega`