A sharp induced emf of $12 \mathrm{V}$ is produced in a given coil when the steady current flowing t

Question

A sharp induced emf of $12 \mathrm{V}$ is produced in a given coil when the steady current flowing through it changes from $5 \mathrm{A}$ to $2 \mathrm{A}$ in exactly $0.5 \mathrm{milliseconds}$. What is the self-inductance of this coil?

Professor PC Thomas Classes · Answer

(c) : The magnitude of induced emf due to self-induction is given by $|\varepsilon| = L \left| \frac{di}{dt} ight|$. We are given $|\varepsilon| = 12 \mathrm{V}$, change in current $|di| = |2 - 5| = 3 \mathrm{A}$, and time interval $dt = 0.5 	imes 10^{-3} \mathrm{s}$. Substituting the values to find $L$: $L = \frac{|\varepsilon|}{|di/dt|} = \frac{12}{3 / (0.5 	imes 10^{-3})} = \frac{12}{6000} = 2 	imes 10^{-3} \mathrm{H} = 2 \mathrm{mH}$.