When an inductor L and a resistor R in series are connected across a 12V, 50Hz supply of current of 0.5 A flows in a circuit. The current differs in phase from applied voltage to `pi/3` radins calculate the value of R.

Explanation

`E_v = 12 V`
`v = 50 Hz`
` I = 0.5 A`
Z
`= E_v/I_v = 12/(0.5) =24Omega`
`phi=pi//3`rad
we know `tan phi = X_L/R`
`tan pi//3 = X_L/R`
`sqrt3= X_L/R`
`X_L=sqrt3R`
Now Z
`=sqrt(R^2+X_L^2)`
`" 24 "`
`= sqrt(R^2(sqrt3R)^2)`
`sqrt(4R^2)=24`
`2R =24`
R
`24/2 =12Omega`