Assignment:
Question 1. A circuit has a branch with three resistors in series of 2, 3, and 8 ohms respectively, connected in series. What is the equivalent resistance of the branch?
Question 2. A circuit has two resistors in parallel, 4 ohms each. Can they be replaced by a single resistor? If so, what would be the equivalent value?
Question 3. What is the energy stored in a 10 F capacitor at t = 4 seconds if v(t) = 2 + 3t ?
Question 4. Using the definition of the Laplace transform, find the Laplace transform of f(at).
Question 5. What is the inverse Laplace transform of 1/s^3?
Question 6. Find the Laplace transform of e^(-3t)cos4t.
Question 7. Determine the inverse Laplace Transform of H(s) = s/(s^2 - 1).
Question 8. The transfer function for a circuit is H(s) = 1/(s+4). What is the natural response of the system?
Question 9. The transfer function for a circuit is H(s) = (s+2)/((s+2)^2 + 4)). What is the natural response of the system?
Question 10. 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?
Provide complete and step by step solution for the question and show calculations and use formulas.