Two identical inductors are connected in two different configurations $P$ and $Q$, where a time vary

Question

Two identical inductors are connected in two different configurations $P$ and $Q$, where a time varying current $I(t)$ is flowing, as shown in the figure. The induced emf between points $a$ and $b$ for configuration $P$ is $E_{P}$ and that for configuration $Q$ is $E_{Q}$. The ratio $E_{P}/E_{Q}$ is:

[Neglect the effect of mutual inductance.]

Accepted Answer

Sol. [Key Concept: Inductors combined in series and parallel] In figure ( $P$ ) $$\begin{array}{r} E_{P} = E_{ab} = - \frac{LdI(t)}{dt}\#(1) \end{array}$$In figure (Q)$$\begin{array}{r} E_{Q} = E_{ab} = - \frac{L}{2}\frac{dl(t)}{dt}\#(2) \end{array}$$$$\ \Rightarrow \frac{E_{P}}{E_{Q}} = \frac{2}{1}$$

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