# Natural and forced response

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

A capacitor integrates current

Capacitor i-v equation in action

### Inductor

### RC

RC natural response — intuition

RC natural response — derivation

RC natural response — intuition

RC natural response — derivation

### RC step response

RC step response — example (3)

### Sketching exponentials

Sketching RC exponentials — examples

### RL

### 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)

### RLC

RLC natural response — intuition