# An inductor and a capacitor with a state

Hi.

Is it correct to say that an inductor with a state, that is some level of current inside it, and a capacitor with some voltage, are equivalent to a current source (in the case of an inductor) and a voltage source (in the case of a charged capacitor) respectively at that instant of time?
Of course the current source and voltage source would not be constant but as described by the exponential decay and rise functions for the transient behaviour.

I was wondering if this equivalence can hold to the extent where we can just draw current sources and voltage sources with the exponential decay and rise functions? Because we know the current source model (ideal) delivers current and the voltage across it is a function of the network it is connected to, likewise, the voltage source supplies voltage and the current across it is a function of the network it is connected to.

When doing transient analysis questions I obviously noticed that the voltages across inductances could change instantaneously, and the same for currents in a capacitor, not accurate for the real situation but for modelling purposes? I am thinking why not because a zero current inductance is modelled as an open circuit, and a zero volt capacitor modelled as a short. Which is the entire purpose of such abstractions like short, open, voltage and current source.

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Baluncore
Yes, everything is an instant source for an instant approximation.

I was wondering if this equivalence can hold to the extent where we can just draw current sources and voltage sources with the exponential decay and rise functions?
It is usually more difficult to model things as exponential sources than to model them as R, C & L components with calculus where R, L & C are fixed coefficients in the integral and differential equations.

When doing transient analysis questions I obviously noticed that the voltages across inductances could change instantaneously, and the same for currents in a capacitor, not accurate for the real situation but for modelling purposes?
If that was a question? Yes, theoretical transient analysis is theoretical. But you must consider that;
Real inductors have series resistance and terminal capacitance.
Real capacitors have series resistance and lead inductance.
Real resistors have lead inductance and terminal capacitance.

dlgoff, berkeman and K Murty