Answer to Question #163169 in Electricity and Magnetism for Lizzy

Question

An alternating pd 220V amplitude and frequency 50Hz is applied to a series circuit containing R=400 ohms, L=0.35H and C= 18 micro farad (a) what is Z? (b) what is the current amplitude ,is it lagging the supply pd (c) what is the power factor?

Answer 1

Given,

Potential difference (V)=220V

$(f)=50Hz$

$R=400 \Omega$

$L=0.35H$

$C= 18 \mu F$

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

$=\sqrt{400^2+({2\pi fL-\frac{1}{2\pi f c})^2}}$

$=\sqrt{16\times 10^4+(2\pi \times 50\times 0.35-\frac{1}{2\pi \times 50\times 18\times 10^{-6}})^2}$

$=\sqrt{16\times 10^4+(35\pi-176.92})^2$

$=\sqrt{16\times10^4+(109.9-176.9)^2}$

$=\sqrt{16\times^4+4489}$

$=\sqrt{160000+4489}\Omega$

$=$ $405.6\Omega$

$i=\frac{V_o}{Z}A$

$=\frac{220}{405.6}A$

$=0.54A$

Power factor $\cos(\phi) = \frac{R}{Z}$

$\cos\phi=\frac{400}{405.6}$

$=0.98$