Characteristic time constant

Definition

The characteristic time constant in an RL circuit, denoted as $\tau$, is the time it takes for the current to reach approximately 63% of its final value after a sudden change in voltage. It is calculated as the ratio of inductance $L$ to resistance $R$, i.e., $\tau = \frac{L}{R}$.

5 Must Know Facts For Your Next Test

1. The characteristic time constant $\tau = \frac{L}{R}$ determines how quickly an RL circuit responds to changes in voltage.
2. In one time constant, the current in an RL circuit will reach about 63% of its maximum value during a transient response.
3. After five time constants ($5\tau$), the current can be considered to have reached its steady-state value.
4. A larger inductance $L$ or smaller resistance $R$ results in a longer time constant, meaning slower response.
5. $\tau$ is a key parameter when analyzing both the charging and discharging phases of an RL circuit.

Review Questions

• How is the characteristic time constant $\tau$ calculated for an RL circuit?
• What percentage of its final value does the current reach after one time constant?
• How does increasing resistance affect the characteristic time constant of an RL circuit?

Related terms

Inductance: A property of an electrical conductor which opposes a change in current, measured in henrys (H).

Resistance: A measure of how much a component reduces the flow of electric current, measured in ohms ($\Omega$).

Transient Response: The behavior of an electrical circuit immediately after a change in voltage or current, before reaching steady-state.