When a series combination of inductance and resistance are conneted with a 10 V, 50 Hz a.c. source, a current of 1 A flows in the circuit. The voltage leads the current by a phase angle of `pi//3` radian. Calculate the values of resistance and inductance.

Explanation

`E_(v) = 10 V, v = 50 Hz, I_(v) = 1 A`,
`Z = sqrt(R^(2) + X_(L)^(2)) = (E_(V))/(I_(v)) = (10)/(1) = 10 Omega`
`tan phi = (X_(L))/(R ) = tan pi//3 = sqrt3`
`:. X_(L) = sqrt3 R`
Put in (i)
`sqrt(R^(2) + 3T^(2)) = 10` i.e., `2 R = 10, R = 5 Omega`
`X_(L) = sqrt3 R = sqrt3 xx 5 ohm`
As `X_(L) = 2 pi v L`
`:. L = (X_(L))/(2 pi v) = (sqrt3 xx 5)/(2 pi xx 50)`
`= 2.757 xx 10^(-2) H = 27.57 mH`