Two coils A and B are connected in series across a $240V, 50H_Z$ supply. The resistance of A is 5 Ω and inductance of B is 0.015H. If the input from supply is 3kW and 2Kvar, find inductance of A and resistance of B. Calculate voltage across each coil.
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$P = 3kW \\ Q = 2KVAR \\ \tan^{-1}⁡∅= \dfrac QP= \dfrac 23=0.67 \\ ∅= \tan^{-1}⁡(0.67) \\ = 33.690 \\ P = V. I. \cos⁡∅ \\ 3000 = 240×I × \cos⁡(33.69) \\ I=15.02A \\ Z_T= \dfrac VI= \dfrac{240}{15.02}=15.98Ω \\ \bar{Z}_T ̅ = Z_T ⦟ ∅ \\ = 15.98 ⦟ 33.69 …