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A.C. Fundamentals - impulse response of series R-L Ciruit

1 Answer

In the context of electrical circuits, an impulse response refers to the behavior of the circuit when an ideal impulse (infinitesimally short-duration pulse) is applied as an input. When dealing with the impulse response of a series R-L (resistor-inductor) circuit, we're essentially studying how the circuit responds to an instantaneous change in voltage or current.

A series R-L circuit consists of a resistor (R) and an inductor (L) connected in series. When an impulse voltage is applied to this circuit, it generates an impulse current response due to the inductor's nature of resisting changes in current. The impulse response of this circuit can be calculated using differential equations and Laplace transforms.

The circuit's response over time is given by the equation:


(

)
=




⋅

−


⋅

(

)
i(t)=I
max
    ​

⋅e
−
τ
t
    ​

⋅u(t)

Where:


(

)
i(t) is the current at time

t




I
max
    ​

 is the peak current that the circuit reaches

τ is the time constant of the circuit, which is equal to

/

L/R, where

L is the inductance and

R is the resistance

(

)
u(t) is the unit step function, which is 0 for

<
0
t<0 and 1 for

≥
0
t≥0

In the context of the impulse response, you can consider an impulse voltage as an input, and the resulting current response will be the impulse response of the circuit. However, due to the mathematical complexities involved, it's more common to analyze step responses or sinusoidal responses in practical scenarios.

For step responses, you would analyze how the circuit reacts when a step change in voltage is applied as input. For sinusoidal responses, you would analyze the behavior of the circuit when a sinusoidal voltage signal is applied as input.

Remember that practical circuits may also involve resistance, inductance, and capacitance (RLC circuits), which can give rise to even more intricate responses when subjected to different types of inputs.
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