Question bank/JEE Main/Physics

In the given A.C. circuit, if battery voltage is
$V = 200\sqrt{2}sin(100\pi t)$, power delivered by battery will have a
power factor of

A$\frac{1}{2}$B$\sqrt{\frac{3}{10}}$C$\frac{3}{\sqrt{10}}$D$\frac{1}{\sqrt{10}}$

Show answer and solution▾

$i_{1} = \frac{200\sqrt{2}}{\sqrt{30^{2} + 40^{2}}}sin(\omega t - \tan^{- 1}(\frac{40}{30}))$
$= 4\sqrt{2}sin(100\pi t - 53^{\circ})$
Phasor diagram
$\Rightarrow tan\theta = \frac{R_{y}}{R_{x}} = \frac{1}{3} \Rightarrow cos\theta = \frac{3}{\sqrt{10}}$

Source: Grass-G / P-17 Physics paper 26 Nov Second.docx