#### (Solved): Exercise 1 (30 Pts) For The RL Circuit Shown In Figure 1, Determine The Transfer Functions V (5)/V ( ...

I need help with second exercise (I just want the answer before matlab part

Exercise 1 (30 pts) For the RL circuit shown in Figure 1, determine the transfer functions V (5)/V (s), V:(s)/V,(s), and I(5)/V (s) where VR is the voltage across the resistor and VL is the voltage across the inductor. Work in the Laplace domain where every element can be treated as an impedance. What is the eigenvalue and how does it relate to how this system behaves? Working in the Laplace domain, if the supply voltage is a unit step input, determine the voltage across the inductor V. (s) and the current flow I(s). Use the final value theorem in the Laplace domain) to determine expressions for the steady state values of the voltage across the inductor and the current flow. If R = 51 and L = 0.01 H, use the provided Matlab script (first_order_responses.m) to plot the time response of the voltage across the inductor and the current flow and compare their final values to the ones you compute from the expressions you obtained above using the final value theorem. Exercise 2 (30 pts) For the RLC circuit shown in Figure 2, determine the transfer functions V:(s)/Vin(s), V(5)/Vin(s), and I(s)/Vin(s) where VL is the voltage across the inductor and Vc is the voltage across the capacitor. If the supply voltage is a unit step input, use the final value theorem (in the Laplace domain) to determine expressions for the steady state values of the voltage across the inductor, the voltage across the capacitor, and the current flow. if R = 502, L = 0.1 H, and C = 5 x 10-6F, use the provided Matlab script (second_order_responses.m) to determine the values of the eigenvalues. Do you anticipate oscillations to exist in the system response? Plot the time response of the voltage across the inductor, the voltage across the capacitor, and the current flow, and compare each of their final values to the ones you compute based on the final value theorem. mm RL le Figure 2. Circuit for Exercise 2.