gen-define-inductor-behavior-in-an-rl-circuit-and-give-one-short-8f4c

Define inductor behavior in an RL circuit and give one short worked example.

# Inductor Behavior in an RL Circuit ## Key Principles An **inductor** opposes changes in current according to: $$V_L = L\frac{di}{dt}$$ where: - V_L = voltage across inductor - L = inductance (henries) - di/dt = rate of change of current ## In RL Circuits When a DC voltage is applied or removed: **Current through inductor:** $$i(t) = \frac{V}{R}(1 - e^{-t/\tau}) \quad \text{(charging)}$$ $$i(t) = I_0 e^{-t/\tau} \quad \text{(discharging)}$$ **Time constant:** τ = L/R --- ## Worked Example **Problem:** A 12V battery is connected in series with R = 6Ω and L = 3H. Find the current at t = 1s. **Solution:** Time constant: τ = L/R = 3/6 = 0.5 s Final current: I_final = V/R = 12/6 = 2 A At t = 1s: $$i(1) = 2(1 - e^{-1/0.5})$$ $$i(1) = 2(1 - e^{-2})$$ $$i(1) = 2(1 - 0.135)$$ $$i(1) = 1.73 \text{ A}$$ The current reaches 86.5% of its final value after 1 second (which is 2τ).