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The RL Circuit
If a coil with inductance L is connected in series with a resistor of resistance R to a source with emf V, the current in the circuit will increase in accordance with the following formula:
I(t) = (V/R)(1 - exp(-t/τ)) ,
where τ = L/R is the time constant (relaxation time) of the R - L circuit. Note that the maximum value of the current Imax = V/Rwill be reached in a time far greater than τ. In a time t = τ, the current l will constitute (l - 1/e) = 0.63 of its maximum value. The reason for the smoothness in the change of the current is the self-induced emf of the coil.
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