Physics

When you connect an inductor and resistor to a battery, the current doesn't jump instantly to its final value—the inductor resists changes in current. The key is using the $RL$ circuit equation $i(t) = \frac{V}{R}(1 - e^{-t/\tau})$, where the time constant $\tau = L/R$ sets how quickly the current grows. Find $\tau$, then solve for the time when current reaches 1.0 A.

When you connect an inductor and resistor to a battery, the current doesn't jump instantly to its final value—the inductor resists changes in current. The key is using the $RL$ circuit equation $i(t) = \frac{V}{R}(1 - e^{-t/\tau})$, where the time constant $\tau = L/R$ sets how quickly the current grows. Find $\tau$, then solve for the time when current reaches 1.0 A.