Problem 1

The switch in the circuit shown has been in position a for a long time. At t = 0, the switch is thrown to position b.

a) Find I, V₁, and V₂ as rational functions of s.

b) Find the time-domain expressions for i, v₁, and v₂.

Problem 2

The energy stored in the circuit shown is zero at the time when the switch is closed.

a) Find the s-domain expression for I.

b) Find the time-domain expression for i when t > 0.

c) Find the s-domain expression for V.

d) Find the time-domain expression for v when t > 0.

Problem 3

The dc current and voltage sources are applied simultaneously to the circuit shown. No energy is stored in the circuit at the instant of application.

a) Derive the s-domain expressions for V₁ and V₂.

b) For t > 0, derive the time-domain expres-sions for v₁ and v₂.

c) Calculate v₁(0⁺) and v₂(0⁺).

d) Compute the steady-state values of v1 and v2.

Problem 4

The initial charge on the capacitor in the circuit shown is zero.

a) Find the s-domain 'Thevenin equivalent cir-cuit with respect to terminals a and b.

b) Find the s-domain expression for the current that the circuit delivers to a load consisting of a 1H inductor in series with a 2 Ω resistor.

Problem 5

There is no energy stored in the circuit in Fig. P13.27 at the time the sources are energized.

a) Find 11(s) and 12(s).

b) Use the initial- and final-value theorems to check the initial- and final-values of ii(t) and i2(t).

c) Find ii(t) and i2(t) for t 0.

Problem 6

The initial energy in the circuit in Fig. P13.29 is zero. The ideal voltage source is 600u(t) V.

a) Find V_o(s).

b) Use the initial- and final-value theorems to find v_o(0⁺) and v_o(∞).

c) Do the values obtained in (b) agree with known circuit behavior? Explain.

d) Find v_o(t).

Problem 7

a) Derive the numerical expression for the transfer function V_o/I_g, for the circuit shown.

b) Give the numerical value of each pole and zero of H(s).

Problem 8

a) Find the numerical expression for the trans-fer function H(s) = V_o/V_i for the circuit in Fig. P13.49.

b) Give the numerical value of each pole and zero of H(s).

Problem 9

Find the numerical expression for the transfer function (V_o/V_i) of each circuit in Fig. P13.50 and give the numerical value of the poles and zeros of each transfer function.