We have now considered four ideal circuit elements. The voltage across each type of element depends in a different way upon the charge passing through it:
|Battery||V is equal to the voltage of the battery, regardless of the current.|
|Capacitor||V = Q / C. The voltage is proportional to the charge on the capacitor.|
|Resistor||V = I R. The voltage is proportional to the current = rate of change of the charge.|
|Inductor||V = L (DI / Dt) . The voltage is proportional to the rate of change of the current.|
A resistor keeps the charge from changing suddenly in a circuit, because an instantaneous change in the charge would require an infinite current which would require an infinite voltage.
A capacitor keeps the voltage from changing suddenly, since the change in charge is the product of the current times the time interval.
An inductor keeps the current from changing suddenly, since an instantaneous change in the current would generate an infinite voltage across the inductor.
In circuits containing only these four elements, wired together in arbitrary ways, after very long times the currents will no longer be changing. (The length of time you have to wait for this is a time that is long compared to the time constants RC and L/R.) In this limit, inductors will have zero voltage across them; but they may have currents flowing through them. Meanwhile, capacitors will have zero currents through them, since a constant current other than zero would build up an infinite charge on them; but they may have voltages across them.
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