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I understand that inductor current and capacitor voltage cannot change abruptly, but can inductor voltage and capacitor current change abruptly?

I have a feeling the answer is no but I cannot explain why.

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In an ideal world, where a capacitor has no series inductance and an inductor has no parallel capacitance, and voltage and current sources can provide voltages and currents with a step-shaped profile, the current into a capacitor and the voltage over an inductor can change abruptly.

Not that this ideal world is an mathematical abstraction, you can't buy such components.

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  • \$\begingroup\$ Thank you. I am only doing mathematical abstractions at this point of my education, so that's completely fine. \$\endgroup\$ – user53172 Sep 13 '14 at 17:46
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but can inductor voltage and capacitor current change abruptly?

Yes, in the context of ideal circuit theory. Indeed, this is often the case when there is a switch in the circuit.

Mathematically, if the slope of inductor current (capacitor voltage) changes abruptly, the inductor voltage (capacitor current) is discontinuous.

So, for example, consider the case that a charged capacitor, an open switch, and a resistor are in series (as in problem 2 here)

At the instant the switch is closed, the voltage across the resistor instantaneously changes from zero to the initial capacitor voltage \$V_0\$. Thus, the capacitor current discontinuously changes from zero to non-zero and is given by

$$i_C(t) = \frac{V_0}{R}e^{-\frac{t}{RC}} \cdot u(t)$$

where \$u(t)\$ is the unit step function

The dual of this is an inductor, with non-zero current \$I_0\$, in parallel with a closed switch and a resistor. At the instant the switch is opened, the current through the resistor changes instantly from zero to the initial inductor current. Thus, the inductor voltage discontinuously changes from zero to non-zero and is given by

$$v_L(t) = I_0R\;e^{-\frac{tR}{L}} \cdot u(t) $$

In physical circuits, voltages and currents cannot instantaneously change but depending on the characteristic time scale, they can effectively change instantaneously.

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I = C*dv/dt. So a step of voltage on a capacitor (infinite dv/dt) leads to infinite current. The response to a step of current is 1/C times the integral of the current. The integral of a step is a ramp, so the capacitor voltage will ramp linearly in response to a step of current. (From whatever initial condition voltage is on it.)

An inductor's response is analogous with current and voltage switched.

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