# Natural and forced response

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.

### Contents

### 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 natural response —– example

### RC step response

Forced response — can be defined two ways

Differential equation theorem — essential part of the step response derivation

RC step response —– example (3)

### Sketching exponentials

Sketching RC exponentials — examples

### RL

RL natural response — intuition

RL natural response — derivation

### 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

Special topics in DC analysis $\qquad$ AC analysis