When an inductor L and a resistor R are connected across 12 V, 50 Hz a.c. supply, a current of 0.5 A flows through the circuit. What is the value of R if current differs in phase from applied voltage by `pi//3` radian?

Explanation

Given `epsilon_("rms") = 12 V f = 50 Hz`
`I_("rms") = 1A `
Phase angle `Phi = pi //3 ` radians
Impedance of the circuit Z ` =(epsilon_("rms"))/(I_("rms"))= (12)/(1) = 12 Omega `
We know that
`cos Phi = ( R)/(Z )`
`implies R = Z cos Phi = 12 cos (pi)/(3)`
= 6 `Omega`