As we know, capacitors and inductors are most important components in circuit design.

I am just curious about how they will behave when connected across voltage or current source as per below image and voltage and current wave-forms in each case.

PS: This can be tutorial question for most of the Electronics learner like us.

Capacitors Inductors

  • \$\begingroup\$ Should there be a switch in each circuit that closes at t=0, or should it be assumed the circuits have been closed for a long period? \$\endgroup\$
    – Chu
    Commented Apr 13, 2016 at 6:58
  • \$\begingroup\$ Yes. Wave-forms will be add on for understanding. :) \$\endgroup\$ Commented Apr 13, 2016 at 7:03
  • \$\begingroup\$ Any half-decent simulator could plot those for you. \$\endgroup\$ Commented Apr 13, 2016 at 7:54

3 Answers 3


There are only two formula that fully encapsulate the theory of inductors and capacitors in AC circuits and transient circuits. Understanding these formulas is more important than trying to ring-fence capacitor and inductor behavior by four trivial scenarios.

For an inductor \$V = L \dfrac{di}{dt}\$ or put another way...

If voltage is constant across an inductor, then \$\dfrac{di}{dt}\$ is constant.

This means current will ramp up to infinite amps unless current is limited.

For a capacitor \$I = C \dfrac{dv}{dt}\$ or put another way...

If current is constant through the capacitor, then \$\dfrac{dv}{dt}\$ is constant.

This means voltage will ramp up to infinity unless voltage is limited.


Case 1: voltage across C is V, current is 0. Case 2: voltage across L is 0, current is I.

With the assumption of ideal sources.

Derivation using the impedance: Z_C=1/(jwC), Z_L=jwL, where w in DC is 0 -> replace C with open circuit and L with short circuit.


1a: At \$\small t=0\$, I is an impulse of strength VC that charges the capacitor instantaneously to V. Thereafter, \$\small I=0\$.

1b: A constant current, I, flows from \$\small t=0\$; the voltage across C increases linearly with time (until the dielectric breaks-down).

2a: Current increases linearly with time (until something melts), satisfying \$ V=L\frac{di}{dt}\$ or \$ \frac{di}{dt}=\frac{V}{L}\$

2b: At \$\small t=0\$ a voltage impulse of strength \$\small IL\$ is generated (by induction), thereafter \$\small V=0\$ and a steady current, I, flows. Zero voltage is required from the current generator to support this current.


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