Video: Finding the EMF Induced in a Coil with a Time-Varying Current

A coil with a self-inductance of 3.0 H carries a current that decreases at a uniform rate d𝐼/d𝑡 = −0.050 A/s. What is the emf induced in the coil?

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Video Transcript

A coil with a self-inductance of 3.0 henries carries a current that decreases at a uniform rate d𝐼 d𝑡 equals negative 0.050 amps per second. What is the emf induced in the coil?

We can call the coil’s self-inductance, 3.0 henries, capital 𝐿. We already have a name for the rate of change of the current. d𝐼 d𝑡 equals negative 0.050 amps per second. We want to solve for the emf that’s induced in the coil.

Starting with a sketch of the coil, our coil, which has some number of loops, has a current 𝐼 that runs through each loop. The emf that is induced in the loop as the current changes in time is given by the mathematical equation 𝑣, the voltage or emf, is equal to the negative of the self-induction of the coil multiplied by the time rate of change of the current.

Applied to our scenario, the emf is equal to negative the self-inductance multiplied by d𝐼 d𝑡, both of which we’ve been given in the problem statement. So we’re ready to plug in and solve for emf. When we do and multiply these two values together, we find that, to two significant figures, emf is 0.15 volts. That’s the electromotive force induced in the coil.

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