# Solved Problems-21

Problems-21

Find the response current of a series

*RL*circuit consisting of a resistor*R*= 3Î© and an inductor*L*= 1 H when each of the following driving force voltage is applied:- unit ramp voltage ,
- unit impulse voltage ,
- unit step voltage ,
- unit doublet voltage , and
- pulse of width
*a*and magnitude 1V beginning at time*t*= 2 seconds.

Solution

- Unit ramp voltage

Applying KVL to

*RL*series circuit,Taking Laplace transform,

Substituting the values,

âˆ´

âˆ´ K

âˆ´ K

_{2}âˆ´

âˆ´

Taking inverse Laplace transform,

- Unit impulse voltage :

In this case,

Taking Laplace transform,

Taking inverse Laplace transform,

- Unit step voltage

In this case,

Taking Laplace transform,

Taking inverse Laplace transform,

- Unit doublet voltage :

In this case,

Taking Laplace transform,

Taking inverse Laplace transform,

- Pulse of width
*a*and magnitude 1V beginning at time*t*= 2 seconds

In this case,

Taking Laplace transform,

Taking inverse Laplace transform,