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Solved Problems-21

Problems-21
Find the response current of a series RL circuit consisting of a resistor R = 3Ω and an inductor L = 1 H when each of the following driving force voltage is applied:
  1. unit ramp voltage Description: Description: 9604.png,
  2. unit impulse voltage Description: Description: 9636.png,
  3. unit step voltage Description: Description: 9642.png,
  4. unit doublet voltage Description: Description: 9661.png, and
  5. pulse of width a and magnitude 1V beginning at time t = 2 seconds.
Solution
  1. Unit ramp voltage Description: Description: 9670.png
Applying KVL to RL series circuit,
Description: Description: 9676.png
 
Taking Laplace transform,
Description: Description: 9682.png
 
Substituting the values,
Description: Description: 9688.png
∴ Description: Description: 9695.png
∴ K2 
Description: Description: 9701.png
∴ Description: Description: 9710.png
∴ Description: Description: 9716.png
 
Taking inverse Laplace transform,
Description: Description: 9723.png
  1. Unit impulse voltage Description: Description: 9729.png:
In this case,
Description: Description: 9735.png
 
Taking Laplace transform,
Description: Description: 9741.png 
 
Taking inverse Laplace transform,
Description: Description: 9749.png
  1. Unit step voltage Description: Description: 9755.png
In this case,
Description: Description: 9764.png
 
Taking Laplace transform,
Description: Description: 9774.png
 
Taking inverse Laplace transform,
Description: Description: 9783.png
  1. Unit doublet voltage Description: Description: 9789.png:
In this case,
Description: Description: 9796.png
 
Taking Laplace transform,
Description: Description: 9804.png
 
Taking inverse Laplace transform,
Description: Description: 9810.png
  1. Pulse of width a and magnitude 1V beginning at time t = 2 seconds
In this case,
Description: Description: 9816.png
 
Taking Laplace transform,
Description: Description: 9823.png 
Description: Description: 9829.png 
Description: Description: 9835.png
 
Taking inverse Laplace transform,
Description: Description: 9841.png
 




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