An alternating voltage of $220 v o l t$ r.m.s at a frequency of $40 c y c l e / s e c$ is supplied in a circuit containing a pure inductance of $0.01 H$ and a pure resistance of $6 o h m s$ 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

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Solution

Given, $V_{r m s} = 220 v$ , $f = 40 H z \Rightarrow ω = 80 π$
and $L = 0.01 H \Rightarrow X_{L} = ω L = 0.8 π = 2.512 Ω$
$R = 6 Ω \Rightarrow i m p e d e n c e, Z = \sqrt{R^{2} + X_{L}^{2}} = \sqrt{36 + 6.3} = \sqrt{= 43.3} = 6.58$
so rms current $I_{r m s} = \frac{V}{Z} = \frac{220}{6.58} = 33.43 A$
Potential difference across the resistance $V_{r} = I_{r m s} R = 33.43 \times 6 = 200.58 V$
Potential difference across the inductor is $V_{L} = I_{r m s} X_{L} = 33.43 \times 2.512 = 83.97 V$
for time lag , $ω t = {tan}^{- 1} \frac{V_{L}}{V_{R}} = 22.7$
power factor , $cos ϕ = c o s 22.7 = 0.922$

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