Question

Derive an expression for the power, power factor and r.m.s. value for a complex wave. A voltage e = 250 sin ωt + 50 sin(3ωt + π/3)  + 2sin (ωt + 5π/6)  + is applied to a series circuit of resistance 20 Ω and inductance 0.05 H. Derive (a) an expression for the current (b) the r.m.s. value of the current and for the voltage (c) the total power supplied and (d) the power factor. Take ω = 314 rad/s.

Answer 1

For Fundamental

X₁ = ωL = 314 x 0.05 = 15.7Ω; Z₁ = 20 + j15.7 = 25.4 ∠ 38.1ºΩ

For Third Harmonic

(a) Expression for the current is