Question

In an `A.C` circuit the instantaneous values of current and voltage are `I = 120 sin omega t` ampare and `E = 300 sin (omega t + pi//3)` volt respectively. What will be the inductive reactance of series `LCR` circuit if the resistance and capacitve reactrance are 2 ohm and 1 ohm respectively?
A. 4.5 ohms
B. 2 ohms
C. 2.5 ohms
D. 3 ohms

Answer 1

Correct Answer - 1
`I = 120 sin omega t, E = 300 sin (omega t + pi //3)`
Clearly, `phi = pi//3`
Now, `cos phi = (R )/(Z) = cos 60^(@) = (1)/(2) :. Z = 2R`
As `R = 2 Omega, :. Z = 2 xx 2 = 4 Omega , X_(C ) = 1 Omega`
Now `(X_(L) - X_(C ))^(2) = Z^(2) - R^(2) = 4^(2) - 2^(2) = 12`
`X_(L) - X_(C ) = +- sqrt(12) = +- 2sqrt(3)`
`X_(L) = X_(C ) +- 2 sqrt(3) = 1 +- 3.464`
Taking + value, `X_(L) = 1 + 3.464 = 4.465 Omega`