Question

In the circuit of Fig., applied voltage V is given by (0 + j10) and the current is (0.8 + j0.6) A. Determine the values of R and X and also indicate if X is inductive or capacitive.

Answer 1

V = 0 + j10 = ∠90°; I = 0.8 + j0.6 = 1∠36.9° 

As seen, V leads the reference quantity by 90° whereas I leads by 36.9°. In other words , I lags behind the applied voltage by (90° − 36.9°) = 53.1° 

Hence, the circuit of Fig. is an R-L circuit.

Now, Z = V/I = 10 ∠90°/1 ∠36.9° = 10 ∠53.1° = 6 + j8 

Hence, R = 6 Ω and X_L = 8 Ω.