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 — intuition RC step response — derivation Forced response — can be defined two ways Differential equation theorem — essential part of the step response derivation 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 — 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