2vi(t) +vc(t) - www 4Ω н 0.5F 1H mmmm iz(t) + vs(t) 292 Vi(t) + In this circuit, the voltage source is v. (t) = sin 2t and the initial capacitor voltage and inductor current are vc (0)=1V and ₁₂ (0) = 0.5 A. (A) Plot the circuit in Laplace transform. (B) Solve v₁(t) for t→ ∞.

Consider the series RLC circuit in Figure Q4. The initial current is 4A and the initial voltage across the capacitor is 4V. Here L= 1H, R=402 and C=1/3 F. The input is x(t) = 5u(t). x(t) R ww L i(t) I Figure Q4 Using Laplace Transform answer the following questions: i. Find the zero-input, zero-state currents and total current, izi(t), izs (t) and i(t).

Determine the z transform ofthe following n+3 xn) = n3) U (n+3) %3D

Im having some problems with these Laplace transforms of circuits. Thanks for your time.

Question 1: Using Laplace Transform, Find the current I in the RLC-circuit in Figure, where R=160n, L 20 H, C 0.002F (Farad), v(t)-37 sin10t V and the current and charge at t-0 are zeroes. (Hint: Identify the governing differential equation for such circuits from the text book) Solution: v(t)

9. Find the Laplace transform of the waveform shown below a) b) Answer: a) F(s) =[1- e-s - e-3s - e-1$] b) F(s) = [e¬s + e-25 + e-3$ + e-4s - 4e-5s1 %3D

i. Determine from first principles the Laplace Transform of t+2e=t -6s+85-56 ii. Show that f (t) = {4sin (2t) – 6e“} =F+4)(3-4)

The signal shown in Figure 3(b) is the input voltage vi(t) as shown in Figure 3(a). is applied to the circuit. Laplace transform of the output voltage value v0(t) in the circuit in Figure 3(a) find using?

Solve a problem showing the application of Laplace transforms in the field of electrical engineering. The problem should be in circuit analysis, transient analysis, control systems, power systems, or other subfields of EE.

Find the inverse Z-Transform for X(Z) shown below for ROC 1- 03 * 22 – 4z – 4z (2 – 1)(22 – 5z +6) X(Z):