Another Sample ES 250 Second Midterm Exam 1. This circuit has two inputs, vs and is, and one output io. The output is related to the inputs by the equation osiaibv=+s Given the following two facts: The output is io = 0.45 A when the inputs are is = 0.25 A and vs = 15 V. and The output is io = 0.30 A when the inputs are is = 0.50 A and vs = 0 V. The values of the constants a and b are a = _________ and b = ________ A/V. The values of the resistances are R 1 = __________ Ω and R 2 = _________ Ω. 2. Fill in the blanks in the following statements: When R = 9 Ω then _________V. Rv =When R = __________Ω then 5.4 V. Rv =When R = __________Ω then 300 mA. Ri = 3. Determine the values of the node voltages va, vb, vc and vo: va = __________ V, vb = __________ V, vc = __________ V, and vo = __________ V.4. The input to this circuit is the voltage, vs. The output is the voltage vo. The voltage v b is used to adjust the relationship between the input and output. Determine values of R 4 and v b that cause the circuit input and output have the relationship specified by the graph v b = __________ V and R 4 = __________ kΩ. 5. The input to this circuit is the voltage: ()204 V for 0tvt e t−=> The output is the current: ()201.2 1.5 A for 0tit e t−=− − > The initial condition is . Determine the values of the resistance and inductance: ()L0 3.5 Ai =−R = ________ Ω and L = _________ H. 6. The initial inductor current is i(0) = 25 mA. Determine the values of the inductor current at 2, 3, 6 and 9 seconds: i(2) = _________ mA, i(3) = _________ mA, i(6) = _________ mA, i(9) = _________ mA.7. a. When C = 10 F then Ceq = _______F. b. When C = ________F then Ceq = 8 F. 8. This circuit has reached steady state before the switch opens at time t = 0. Determine the values of , ()Lit()Cvt and ()Rvt immediately before the switch opens: (L0i −))))=_________A, =__________V (C0v −and (R0v −=___________V Determine the value of immediately after the switch opens: ()Rvt(R0v +=___________V 9. After time t = 0, a given circuit is represented by this circuit diagram. a. Suppose that the inductor current is ()421.6 28.4 mA for 0tit e t−=+ ≥ Determine the values of 1R and 3R: 1R= ___________ Ω and 3R= ___________ Ω. b. Suppose instead that 1R= 16 Ω , 3R= 20 Ω, the initial condition is i(0) = 10 mA, and the inductor current is . Determine the values of the constants A, B, and a: () for 0atit A Be t−=− ≥ A = ___________ mA, B = ___________ mA and a = ___________ s. 10. a) Determine the time constant, τ, and the steady state capacitor voltage, v(∞), when the switch is open: τ = ___________ s and v(∞) = ___________ V b) Determine the time constant, τ, and the steady state capacitor voltage, v(∞), when the switch is closed: τ = ___________ s and v(∞) = ___________