Answer to Question #212463 in Electricity and Magnetism for Mpho Mathenjwa

Question

A 200 Ω

Ω resistor, a 700 mH inductor and an 6.00 μ

μF capacitor are connected in series with a 240 V, and 60.0 Hz, AC source. Calculate the power factor.

Answer 1

$power\space factor, Cos\phi=R/Z$

$Z=\sqrt{R^2+(X_L-X_C)^2}$

inductive reactance, $X_L=2\pi fl=2\pi \times 60\times700/1000=263.89\Omega$

capacitive reactance, $X_C=\frac{1}{2\pi fc}=\frac{1}{2\pi \times 60\times 6\times10^{-6}}=442.10\Omega$

$Z=\sqrt{200^2+(263.89-442.10)^2}=267.89$

$Cos\phi=R/Z=200/267.89=0.7466$