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

`R=30omega`
`C=0.25 muF = 0.25 xx 10^(-6)F`
` E_v = 100 V `
`omega = 10000` rad/s = `10^4` rad/s
`I_v=?`
`V_R=?`
`V_C= ?`
`Z=sqrt(R^2+X_C^2)`
`= sqrt(R^2+1/(omega^2C^2))`
`Z=sqrt((30)^2+1/((10^4)^2(0.25xx10^(-6))^(2)))`
`=sqrt(9000+1/(10^8xx0.625xx10^(-12)))`
`= sqrt(900+1/(0.625xx10^(-5)))`
`=sqrt(900+1.6xx10^5)`
`= sqrt(900+160000)`
`sqrt(160900)`
`Z = 401.12Omega`
`I_v =E_v/Z = 100/(401.12)=0.249A`
`V_R = I_vR = 0.249xx30`
`= 7.479 ` volt
`V_C = I_vX_C = 0.249xx160000`
`= 39840 =3.9xx10^4 ` volt