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Circuit Analysis

Please provide detailed steps in finding the answers.

1) Find the Laplace transform of e^(−3t) cos 4t.

2) Find the inverse Laplace Transform of s/(s^2 - 1).

3) The transfer function for a circuit is H(s) = (s-1)/((s-1)^2 + 4). What is the natural response of the system? Is it stable?

4) The natural response of a circuit is given by h= cosh t. What is the transfer function?

5) If a current i=40cos(100t+20°)is fed through a 1/10 F capacitor, what voltage is across it?

6) A current i=40cos(100t+20°)is fed through a 1/10 F capacitor. What is the instantaneous power?

7) A current i=40cos(100t+20°)is fed through a 1/10 F capacitor. What is the average power?

8) A 21 V source is in series with a 3 ohm and a 4 ohm resistor. What is the total power absorbed by the 4 ohm resistor?

9) If a capacitor rated at 1/5 F is in series with a 5 ohm resistor, compute the time constant.

10) At time t = 0 , the current flowing through an inductor is i0 . A switch is closed and the inductor is in series with a resistor R . What current flows through the inductor from that time on if there are no sources?

11) At time t = 0 , the voltage across a capacitor is v0 . A switch is closed and the capacitor is in series with a resistor R . What voltage is across the capacitor from that time on if there are no sources?

12) At time t = 0 , the voltage across a capacitor rated at 3/10 F is 10 V. A switch is closed and the capacitor is in series with a resistor R = 50 ohms. How long does it take for the voltage to decay to 4 volts?

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