Transient and Ac Response of Rl Circuits

Contents                                                         Page

1. Transient Response of an RL Circuit..................................................................................(3)

2. Steady-State AC Response of an RL Circuit.......................................................................(6)

3. Practical Application of RC Circuits & RL Circuits..............................................................(9)

1. Transient Response of an RL Circuit

Determined equations for the transient response of a series RL circuit to a step input applied at t=0:[pic 1]

[pic 2]

[pic 3]

[pic 4]

[pic 5]

Appropriate component values to achieve a time constant ( equal to 10 seconds are shown on the following diagram. [pic 7][pic 8][pic 6]

Due to the value of the time constant being equal to the value of the inductor divided by the value of the resistor, , the values are therefore suitable for  = 10s.[pic 9][pic 10]

[pic 11]
[pic 12]

To estimate the time at the point when the resistor voltage () has reached 95% of its final voltage, it can be said that:[pic 13]

[pic 14]

[pic 15]

[pic 16]

[pic 17]

[pic 18]

[pic 19]

[pic 20]

[pic 21]

[pic 22]

The circuit time constant () is 10 seconds, and due to the maximum point being accepted as reached at 5, 95% of the voltage is reached at   of the given time scale. This demonstrates how when the current initially flows through the resistor, the increase in  is relatively fast in comparison to the increase from 3 - 5.[pic 23][pic 24][pic 25][pic 26][pic 27][pic 28]

[pic 29][pic 30]

It can be seen from Fig 2. and Fig 3. that when a step input is applied to an RL circuit that as time progresses, the resistor voltage () increases with time, it's increase slowing exponentially, whereas the inductor voltage () decreases with time, in the same fashion as .[pic 31][pic 32][pic 33]

In relation to the transient response of an RC circuit, it can be seen that the resistor responses are opposite. When connected in an RC circuit,  decreases as time passes,  and the capacitor voltage ( increases, both in the same exponential manner and never completely reaching  the extremities of 10V or 0V.[pic 34][pic 35]