In electrical engineering, the step response of a circuit is the behavior of the circuit when subjected to a sudden change in input, typically from zero to a constant value (step input). In the case of an R-L (resistor-inductor) circuit, the step response refers to how the circuit responds when a step voltage is applied across it.
Let's consider a simple series R-L circuit:
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+---R----L----(Voltage Source)
|
----> Output
Here, R represents the resistance, L represents the inductance, and the voltage source is the step input that changes from 0 to a constant voltage at time t = 0.
When the step voltage is applied at t = 0, the inductor opposes sudden changes in current due to its property of self-inductance. This means that initially, the current through the inductor cannot change instantaneously. It will start to increase gradually from zero, based on the time constant of the circuit.
The time constant (Ď) of an R-L circuit is given by:
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Ď = L / R
Where:
Ď is the time constant in seconds.
L is the inductance in henries (H).
R is the resistance in ohms (Ί).
The response of the current in an R-L circuit can be described by the equation:
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i(t) = (V / R) * (1 - e^(-t / Ď))
Where:
i(t) is the current at time t.
V is the voltage of the step input.
R is the resistance of the circuit.
Ď is the time constant.
Here's what happens during the step response:
At t = 0, the current is zero.
As time progresses, the current starts to increase towards its final value of (V / R).
The current approaches the final value asymptotically, never quite reaching it due to the exponential term in the equation.
In practical terms, the time constant Ď determines how quickly the circuit responds to the step input. A larger inductance or smaller resistance will result in a slower response, while a smaller inductance or larger resistance will lead to a faster response.
Keep in mind that this description assumes ideal conditions and does not account for factors like parasitic capacitance, resistance in the inductor's windings, or mutual inductance if multiple inductors are present in the circuit.