Physics - EMI/AC Question with Solution | TestHub

In inductive circuit, the voltage leads the current by $90^{\circ }$. Therefore,

$$\begin{gathered} {\varphi }_{0\mathrm{V}}-{\varphi }_{0I}=90^{\circ } \\ \Rightarrow {\varphi }_{0\mathrm{V}}=60^{\circ } \end{gathered}$$

From the given equation $5\sin \left(49\pi t-30^{\circ }\right)$, angular frequency $\omega =49\pi rad{\text{s}}^{-1}$

The amplitude of the voltage across the inductor will be,

$V_0=i_0{X}_L$

$\Rightarrow V_0=i_0\left(\omega L\right)$

$\Rightarrow V_0=\left(5\right)\left(49\pi \right)\left(30\times 10^{-3}\right)$ $=23.1$

$\Rightarrow \mathrm{V}=23.1\sin \left(49\pi t+60^{\circ }\right)$