The equation of current in a purely inductive circuit is 5 (49 - 30...

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

${ϕ}_{0V} - {ϕ}_{0I} = 90 ° ⇒ {ϕ}_{0V} = 60 °$

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

The amplitude of the voltage across the inductor will be,

${V}_{0} = {i}_{0}{X}_{L}$

$⇒ {V}_{0} = {i}_{0}\left(\omegaL\right)$

$⇒ {V}_{0} = \left(5\right)\left(49\pi\right)\left(30 \times {10}^{- 3}\right)$= 23 . 1$</p><p>$⇒ V = 23 . 1\sin \left(49\pit + 60 °\right)