Capacitors and inductors store energy. The natural response of a circuit is what it does “naturally” as its internal energy moves around. As the energy sloshes around we track what happens to voltage and current.

If you connect an external energy source to a circuit its behavior changes. The circuit displays a natural response and a forced response. The $\text{RC}$ step response is an example of natural plus forced response.

Capacitor

Capacitor i-v equations

A capacitor integrates current

Capacitor i-v equation in action

Inductor

Inductor i-v equations

Inductor kickback

Inductor kickback (1)

Inductor kickback (2)

RC

RC natural response — intuition

RC natural response — derivation

RC natural response — intuition

RC natural response — derivation

RC natural response — example

RC step response

RC step response

RC step response — intuition

RC step response — setup (1)

RC step response — solve (2)

RC step response — example (3)

Sketching exponentials

Sketching RC exponentials

Sketching RC exponentials — examples

RL

RL natural response

LC

LC natural response — intuition

LC natural response — derivation

LC natural response — intuition (1)

LC natural response — intuition (2)

LC natural response — derivation (1)

LC natural response — derivation (2)

LC natural response — derivation (3)

LC natural response — derivation (4)

LC natural response — example

RLC

RLC natural response — intuition

RLC natural response — derivation

RLC natural response — variations