ES 250 Practice Final Exam 1. Given that a8 Vv =, Determine the values of 1Rand ov : 1R= ____10____ Ω, and ov = ___−3.2___ V 2. Given that 0 ≤ R ≤ ∞ in this circuit, consider these two observations: When R = 2 Ω then Rv =4 V and Ri = 2 A. When R = 6 Ω then Rv =6 V and Ri = 1 A. Fill in the blanks in the following statements: a. The maximum value of Ri is ____4_____A. b. The maximum value of Rv is ____8_____V. c. The maximum value of RRRpiv= occurs when R = _____2____Ω. d. The maximum value of RRRpiv= is ____8____W. 3. 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 = ___1.62__ V and R 4 = ___62.5___ kΩ.4. Consider this inductor. The current and voltage are given by ()5 4.6 0 0.20.2 0.50.5ttit at b tct−≤≤⎧⎪=+ ≤≤⎨⎪≥⎩ and ()12.5 0 0.225 0.2 0.500.5tvt tt<<⎧⎪=<<⎨⎪>⎩ where a, b and c are real constants. (The current is given in Amps, the voltage in Volts and the time in seconds.) Determine the values of the constants: a = ___10___A/s, b = ___−5.6___A and c = ___−0.6__A 5. This circuit is at steady state when the switch opens at time t = 0. The capacitor voltage is ()for 0 atvt A Be t−=+ ≥. Determine the values of the constants A, B, and a: A = ____4__ V, B = __8___ V and a = ____10___ s. 6. This circuit is at steady state before the switch closes at time t = 0. After the switch closes, the inductor current is given by ()50.6 0.2 A for 0 tit e t−=− ≥ Determine the values of 1R, 2Rand L: 1R= ___20____ Ω , 2R= ___10____ Ω and L = ___4____ H 7. The voltage and current for this circuit are given by v(t) = 20 cos (20t + 15°) V and i(t) = 1.49 cos (20t + 63°) ADetermine the values of the resistance, R, and capacitance, C: R = ____9____ Ω and C = ___5_____ mF.8. This circuit is at steady state. The voltage source voltages are given by v1(t) = 12 cos (2t – 90°) V and v2(t) = 5 cos (2t + 90°) V The currents are given by i1(t) = 744 cos (2t – 118°) mA , i2(t) = 540.5 cos (2t + 100°) mA and i(t) = A cos (2t −164°) mA Determine the values of A, 1R, 2R, L and C: A = __460__ mA, 1R = __10__ Ω, 2R = __10__ Ω, L = __6__ H and C = __50__ mF. 9. The input this circuit is the current () ( )s2cos 5 15 Ait t=+°. In the frequency domain, this circuit is represented by the node equation ab0.5 0.5 2 150.5 0.25 0dj jjje⎡⎤+− ∠°⎡⎤⎡⎤=⎢⎥⎢⎥⎢⎥−+⎣⎦⎣⎦⎣⎦VV where aV and bV are the phasor node voltages and d and e are real numbers. Determine the values of d and e. d = ___0.125___Ω and e =
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