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