Physics - EMI/AC Question with Solution | TestHub

Let$\varphi$is the phase difference between$V$and$i$

$\text{tan}\varphi =\frac{X_L}{R}=\frac{\omega L}{R}=\frac{100\times 1}{100}=1$

$\Rightarrow \varphi =\frac{\pi }{4}$

Since this is an$\mathrm{LR}$circuit,$V$will lead$i$

$\therefore$The instantaneous current equation will be

$i_{\mathrm{}}=i_{0 }\text{sin}\left(100 t-\varphi \right)$where$\varphi =\frac{\pi }{4}$and$i_0=\frac{V_0}{Z}$

$i_0=\frac{V_0}{\sqrt{R^2+{\left(\omega L\right)}^2}}=\frac{200}{\sqrt{{\left(100\right)}^2+{\left(100\times 1\right)}^2}}=\sqrt{2}$

$\therefore i=\sqrt{2}\text{sin}\left(100 t-\frac{\pi }{4}\right)$