Network Analysis- BEC304
Module 4: Laplace Transform
1. Find the Laplace transform of the unit step function as shown in Figure
2. Find the Laplace transform of the f(t) = eat where a is constant.
3. Find the Laplace transform of the f(t) = sinωt.
4. Find the Laplace transform of the f(t) = cosωt.
5. Find the Laplace transform i) sin2t ii) cos2t.
6. Find the Laplace transform of the stair case waveform as shown in Figure
7. Find the Laplace transform of the square wave as shown in Figure.
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Network Analysis- BEC304
8. Find the Laplace transform of the waveform as shown in Figure
9. Find the Laplace transform of the waveform as shown in Figure
10. Find the Laplace transform of the waveform as shown in Figure.
11. Find the Laplace transform of the waveform as shown in Figure
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Network Analysis- BEC304
12. Find the Laplace transform of the waveform as shown in Figure
13. Find the Laplace transform of the waveform as shown in Figure
14. Find the Laplace transform of the waveform as shown in Figure
15. Find the Laplace transform of the waveform as shown in Figure.
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Network Analysis- BEC304
16. Find the Laplace transform of the waveform as shown in Figure.
17. Find the Laplace transform of the waveform as shown in Figure.
18. Find the Laplace transform of the waveform as shown in Figure
19. Find the Laplace transform of the waveform as shown in Figure
20. Find the Laplace transform of the waveform as shown in Figure.
21. Find the Laplace transform of the waveform as shown in Figure
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Network Analysis- BEC304
22. In the circuit shown in Figure find an expression for i(t) when the switch K is closed
at t=0.
23. In the circuit shown in Figure find an expression for i(t) when the switch K is closed
at t=0. Assume that there is no initial charge on the capacitor.
24. In the circuit shown in Figure the battery voltage 10 V is applied for a steady state
period with switch K is open. Obtain the expression for the current after closing the
switch K. Use laplace transform.
25. Using Laplace transform obtain expression for the circuit shown in Figure. Assume
zero initial conditions.
26. For the critically related network of the circuit shown in Figure obtain an expression
for i(t). Use Laplace transform.
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Network Analysis- BEC304
27. In the circuit shown in Figure if the capacitor is initially charged to 1 V, find an
expression for i(t), when the switch K is closed at t = 0.Use Laplace transform
28. In the circuit shown in Figure the switch K is closed and steady state is reached. At t =
0 switch K is opened. Find the expression for current i(t) in the inductor using Laplace
transform.
29. Using Laplace method obtain the expression for i(t). The capacitor is zero initially.
Also obtain the expression for the capacitor voltage in S domain for the circuit shown
in Figure
30. In the circuit shown in Figure solve for iL(t) using Laplace transformation.
31. Find the laplace transform of the given function f(t) = 5 + 4e-2t.
32. For the circuit shown in Figure was in steady state before t=0. The switch opened at
t=0. Find i(t) i(t) > 0 using Laplace transform.
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Network Analysis- BEC304
33. Find the current i(t) when switch K is opened at t=0 with the circuit having reached
steady state before the switching in Fig. Find current at t=0.5 sec.
34. Find the current i(t) assuming zero initial conditions when switch K is closed at t=0.
The excitation v(t) is a pulse of magnitude of 10 V and duration of 2 sec. Refer Figure
35. State and prove initial value theorem.
36. State and prove final value theorem.
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