Why is the voltage across a capacitor (as a function of time) continuous? Why is the current across an inductor (as a function of time) continuous?
Answer
If the voltage across a capacitor was discontinuous the charge on the capacitor would be discontinuous which would mean a transfer of charge in an infinitely short period of time i.e. an infinite current.
A similar argument applies for an inductor except this time a discontinuous change in the current would imply an infinite rate of change of current which for an inductor would mean an infinite induced emf opposing the change producing it.
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