# Summarizing Rl Circuits

## Summary

• When a series connection of a resistor and an inductor—an RL circuit—is connected to a voltage source, the time variation of the current is

$$I={I}_{0}(1-{e}^{-t/\tau })\text{(turning on).}$$

where $${I}_{0}=V/R$$ is the final current.

• The characteristic time constant $$\tau$$ is $$\tau =\cfrac{L}{R}$$ , where $$L$$ is the inductance and $$R$$ is the resistance.
• In the first time constant $$\tau$$, the current rises from zero to $$0\text{.}\text{632}{I}_{0}$$, and 0.632 of the remainder in every subsequent time interval $$\tau$$.
• When the inductor is shorted through a resistor, current decreases as

$$I={I}_{0}{e}^{-t/\tau }\text{(turning off).}$$

Here $${I}_{0}$$ is the initial current.

• Current falls to $$0\text{.}\text{368}{I}_{0}$$ in the first time interval $$\tau$$, and 0.368 of the remainder toward zero in each subsequent time $$\tau$$.

## Glossary

### characteristic time constant

denoted by $$\tau$$, of a particular series RL circuit is calculated by $$\tau =\cfrac{L}{R}$$, where $$L$$ is the inductance and $$R$$ is the resistance