A capacitor of `100 muF`, a resistor of `20 Omega` and an inductor of inductance L are connected in series with an a.c. source of frequency 50 Hz. Calculate the value of inductance L of the inductor, if phase angle between current and voltage is zero.

Explanation

`C = 100 muF = 100 xx10^(-6)F`
`C = 10^(-4)F`
`R = 50 Omega`
`L=0.5 H`
`E_v = 110 V`
`v= 50 Hz`
`I_v= ?`
`Z=sqrt(R^2+(X_L-X_C)^(2))=sqrt((R^2+(2pivL-1/(2pivC))^(2)`
`Z = sqrt((50)^2+(2xx3.14xx50xx0.5-1/(2xx3.14xx50xx10^(-4)))^(2))`
`Z= sqrt(2500+(157-3.184)^(2))`
`= sqrt(2500+(125.16)^(2))=sqrt(2500+15665.03)`
`= 134.77 Omega`
`I_v = E_v/Z = 110/(134.77)= 0.82A`