Capacitors and inductors store energy. Voltage and current change over time as the energy moves around.

The natural response of a circuit is what it does “naturally” with internal energy and no external energy source.

When you connect an external energy source the behavior includes both the 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