The equation of current in a purely inductive circuit is 5 sin 49 π t - 30 ° . If the inductance is 30 mH then the equation for the voltage across the inductor, will be

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In inductive circuit, the voltage leads the current by $90 °$ . Therefore,
$ϕ_{0 V} - ϕ_{0 I} = 90 ° \Rightarrow ϕ_{0 V} = 60 °$
From the given equation $5 \sin (49 π t - 30 °)$ , angular frequency $ω = 49 π rad s^{- 1}$
The amplitude of the voltage across the inductor will be,
$V_{0} = i_{0} X_{L}$
$\Rightarrow V_{0} = i_{0} (ω L)$
$\Rightarrow V_{0} = (5) (49 π) (30 \times 10^{- 3})$ $= 23.1$
$\Rightarrow V = 23.1 \sin (49 π t + 60 °)$

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