Exercise

EXERCISE

1. A series RL circuit with R = 10Ω and L = 0.2H has a constant voltage V = 50V applied at t = 0. Find the resulting current using the Laplace transform method.

[Ans: I = 5 - 5e^-50t Al

2. For the circuit shown in fig.3.36, determine the current when the switch is closed at t = 0. Assume zero charge on the capacitor initially.

3. A series RLC circuit with R = 52 and L = 0.1 H and C = 500 μF has a constant voltage V = 10V applied at t = 0. Find the resulting current.

[Ans: i = 0.72 e^-25t sin 139t A]

4. For the circuit shown in fig.3.37, the switch is closed at t = 0. Find i2 (t) for t> 0. Assume zero initial energy. Use Laplace transform technique.

 [Ans: i₂ (1) = 3.33-5e^-10t + 1.67 e-^30t]

5. A voltage of 100V DC is applied to a series circuit consisting of R and C = 50 μF. If the voltage across C is observed to be 50V at t = 1 sec, determine the value of R in the circuit. Sketch the waveform of voltage across C.

[Ans: R= 28.854 KΩ]

6. A series RLC circuit with R = 59, L = 0.1H and C = 500 μF has a sinusoidal voltage source V = 100 sin (250t+) volts. Find the resulting current if the switch is closed when = 0°.

[Ans: i = e^-25t (5.42 cos 139t + 1.89 sin 1391) + 5.65 sin (250t - 73.6°)A]

7. In the network shown in fig.3.38. below, the switch is closed at t = 0 and there is no initial charge on either of the capacitors. Find the resulting current i (t) using Laplace transformation.

8. If the capacitors are uncharged and the inductor current is zero at t = 0 in the network shown in Fig.3.39 below, show that the transform of the generation current is

9. Find current i, as a time function in circuit shown in Fig.3.40 using (i) loop current method, (ii) nodal voltage method.

Assume all initial conditions to be zero.

[Ans : 3 (1 – e^-t - e^-2t + e^-3t) amp.]

 [Note: The student may proceed for solving the problem after drawing the circuit diagram in s- domain.]