An alternating current of 1.5 mA and angular frequency `omega = 300` `radian//sec` flows through `10 k Omega` resistor and a `0.50 mu F` capacitor in series. Find the r.m.s. voltages across the capacitor and impedance of the circuit.

Explanation

Here, `I_(v) = 1.5 mA = 1.5 xx 10^(-3) A`,
`omega = 300 rad//s, R = 10 k Omega = 10^(4) Omega`,
`C = 0.5 mu F = 0.5 xx 10^(-6) F`
`X_(C ) = (1)/(omega C) = (1)/(300 xx 0.5 xx 10^(-6)) = (10^(6))/(150)`
`= (20)/(3) xx 10^(3) Omega`
`Z = sqrt(R^(2) + X_(C )^(2)) = sqrt(10^(8) + (4)/(9) xx 10^(8))`
` = 10^(4) sqrt((13)/(9)) = 1.2 xx 10^(4) Omega`
rms voltage across the capacitor
`= I_(v) X_(C ) = 1.5 xx 10^(-3) xx (20)/(3) xx 10^(3) = 10 `volt