Question

An alternating emf e = 100 sin [2π(1000) t] (in volt) is applied to a series LCR circuit with resistance 300 Ω, inductance 0.1 H and capacitance 1 µF. Find the power factor and the average power consumed over one cycle.

Answer 1

Data: e = 100 sin[2π (1000)t] (in volt), R = 300 Ω L

= 0.1H, C = 1 µF = 1 × 10^-6 F

Comparing e = e₀ sin 2πft with the given equation,

we get e₀ = 100 V, f = 1000 Hz

∴ X_L = 2πfL = 2(3.142)(1000)(0.1) = 628.4 Ω

Impedance, Z = \(\sqrt{R^2+X^2}\)

The power factor, cos ϕ  = \(\cfrac{R}Z\) = \(\cfrac{300}{557}\) = 0.5386

The average power consumed over one cycle