In a series RC circuit, R = 30 ohm, `C = 0.25 mu F`, `V = 100 V, omega = 10000 rad//s`. Find the current in the circuit and calculate the voltage across the resistor and capacitor. Is the algebraic sum of these voltages more than the source voltage ? If yes, resolve the paradox.

Explanation

Here, `R = 30 Omega, C = 0.25 mu F, E_(v) = 100 V`,
`omega = 10000 rad//s, I_(v) = ?`
`X_(C ) = (1)/(omega C) = (1)/(10000 xx 0.25 xx 10^(-6)) = 400 Omega`
`Z = sqrt(R^(2) + X_(C )^(2)) = sqrt(30^(2) + (400)^(2)) = 401.1 Omega`
`I_(v) = (E_(v))/(Z) = (100)/(401.1) ~= 0.25 A`
`V_(R ) = I_(v) X_(R ) = 0.25 xx 30 = 7.5 V`
`V_(C ) = I_(V) X_(C ) = 0.25 xx 400 V`
`V_(R ) + V_(C ) = 7.5 + 100 = 107.5 V`, which is more than source voltage = 100 V .This is because `V_(R )` and `V_(C )` are not in the same phase.