Question

An alternating voltage of $220volt$ r.m.s at a frequency of $40cycle/sec$ is supplied in a circuit containing a pure inductance of $0.01H$ and a pure resistance of $6ohms$ in series. Calculate (i) the current, (ii) potential difference across the resistance, (iii) potential difference across the induction, (iv) the time tag, (v) power factor

Answer 1

Given, $V_{rms}=220v$, $f=40Hz\Rightarrow \omega =80\pi$

and $L=0.01H\Rightarrow X_L=\omega L=0.8\pi =2.512\Omega$

$R=6\Omega \Rightarrow impedence,Z=\sqrt{R^2+X_L^2}=\sqrt{36+6.3}=\sqrt{=43.3}=6.58$

1. so rms current $I_{rms}=\frac{V}{Z}=\frac{220}{6.58}=33.43A$
2. Potential difference across the resistance $V_r=I_{rms}R=33.43\times 6=200.58V$
3. Potential difference across the inductor is $V_L=I_{rms}{X}_L=33.43\times 2.512=83.97V$
4. for time lag , $\omega t={\tan }^{-1}\frac{V_L}{V_R}=22.7$
5. power factor , $\cos \varphi =cos22.7=0.922$