The equation of current in a purely inductive circuit is 5 sin 49 π t - 30 ° . If the inductance…

In inductive circuit, the voltage leads the current by $90°$. Therefore,

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

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

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$ 

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