Rl Time Constant

Question

Time constant τ for RL circuit (R, L) equals?

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1. **Definition**: The time constant ($	au$) of an RL circuit determines how quickly the current reaches its steady-state value after a switch is closed or opened.
2. **Current Growth Equation**: $I(t) = I_{max} (1 - e^{-t/	au})$.
3. **Derivation**: From Kirchhoff's Loop Law: $\epsilon - L\frac{di}{dt} - iR = 0$. Solving this differential equation reveals $	au = L/R$.
4. **Physical Meaning**: After one time constant ($t = 	au$), the current grows to about $63.2\%$ of its maximum value ($I_{max} = E/R$).
5. **Inversely**: For decay, $I(t) = I_0 e^{-t/	au}$, current drops to $36.8\%$ after $t = 	au$.

Rl Time Constant

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