Question

Draw the impedance triangle for a series LCR AC circuit and write the expressions for the impedance and the phase difference between the emf and the current.

Answer 1

Impedance triangle for a series LCR AC circuit

For a series LCR AC circuit in which ideal components are used, the three phasors are:

`vec e_R = vecRi_0, vece_L = X_Lveci_0` and `vece_C = X_Cveci_0`. For X_L > X_C, the impedance triangle is as shown in the figure. Here,

Z² = R² + (X_L − X_C)²

∴ Z = `sqrt(R^2 + (X_L - X_C)^2` and tan Ø = `(X_L - X_C)/R`

cos Ø =  `R/Z` is called the power factor.