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  4. A resistor of 500 Ω, an inductance of 0.5 H are in series with an AC voltage source which is given by V = 100 √2 sin (1000t). The power factor of the combination is

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Q. A resistor of $500\,\Omega$, an inductance of $0.5\, H$ are in series with an $AC$ voltage source which is given by $V = 100 \sqrt{2}$ sin $(1000t)$. The power factor of the combination is

JIPMERJIPMER 2013Alternating Current

Solution:

Voltage $V=100 \sqrt{2}\, \sin (1000 \,t)$
and $V=V_{0} \sin \,\omega \,t$
On comparing $\omega=1000$
Inductive reactance
$X_{L}=\omega L=1000 \times 0.5=500 \,\Omega$
$\therefore \cos \phi=\frac{500}{\sqrt{(500)^{2}+(500)^{2}}}$
$=\frac{1}{\sqrt{2}}$