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Say there is a circuit with a current source and an inductor. There is a current $i(t) = at$ going through the inductor. We now place a new circuit with an inductor and a resistor next to it. The current $i(t)$ causes a changing magnetic flux - and thus an emf - through this new circuit. Since $i(t)$ is linear, the emf is constant, and the current in the new circuit will also be constant and will not create a changing magnetic flux through the original circuit, so the current in the original circuit doesn't change. In other words, the second circuit received current and energy for free.

Obviously, this can't be true because of the law of conservation of energy. But where does this reasoning go wrong?

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Since 𝑖(𝑡) is linear, the emf is constant, and the current in the new circuit will also be constant and will not create a changing magnetic flux through the original circuit

Here is your mistake. This is correct in the steady state, but not in the transient state when the second inductor is introduced. During that transient state the current will be ramping up from 0 to the steady state current, and there will be an EMF back. This will increase the voltage across the first inductor. The increased voltage will persist, resulting in higher power delivery than if the second inductor were not included.

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  • $\begingroup$ Thank you for your answer, the first part makes sense to me. But why would the increased voltage persist after the second inductor reached a steady state? And where does the extra power come from? $\endgroup$ – Sudera Oct 18 '19 at 14:13

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