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(D) The instantaneous values of $e.m.f.$ $(E)$ and current $(i)$ in a purely inductive circuit are given by $E = E_0 \sin(\omega t)$ and $i = i_0 \sin

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$2\omega$

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(D) The instantaneous values of $e.m.f.$ $(E)$ and current $(i)$ in a purely inductive circuit are given by $E = E_0 \sin(\omega t)$ and $i = i_0 \sin(\omega t - \frac{\pi}{2})$.The instantaneous power $P_{inst}$ is the product of $E$ and $i$:$P_{inst} = E \cdot i = E_0 \sin(\omega t) \cdot i_0 \sin(\omega t - \frac{\pi}{2})$Using the trigonometric identity $\sin(\omega t - \frac{\pi}{2}) = -\cos(\omega t)$:$P_{inst} = E_0 i_0 \sin(\omega t) \cdot (-\cos(\omega t))$$P_{inst} = -E_0 i_0 \sin(\omega t) \cos(\omega t)$Using the double angle identity $\sin(2	heta) = 2 \sin 	heta \cos 	heta$:$P_{inst} = -\frac{1}{2} E_0 i_0 \sin(2\omega t)$The angular frequency of the instantaneous power is the coefficient of $t$ inside the sine function,which is $2\omega$.

An alternating $e.m.f.$ of angular frequency $\omega$ is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency

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