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1. A 1.2 µF capacitor is initially charged to 50V. How much energy is stored in the capacitor? What will be the voltage on the capacitor after it has been discharged by a 10 µA current for two seconds? 2. Consider the circuit below. After the switch has been closed for a long time, determine the value of the currents as referenced in the schematic. R3 = R4 = R5 = 10kΩ, L1 = 1mH, C1 = 100µF. TCLOSE = 0 1 2 R3 i2 i1 R4 is 2 L1 C1 R5 Vs= 10V 1 is = _________ i1 = __________ i2 = __________ 2 3. The switch in the circuit below has been closed for a long time. At t=0 the switch opens. I3 = 5mA, R4 = 10kΩ and C3 = 1.2µF. If the voltage on the capacitor at t=0 is 25V, develop an expression for the voltage across the capacitor V(t) for t>0. Show your work. 5mA Switch open @ t=0 1 I3 R4 10k V(t) + - V(t) = ____________________________ C3 1.2uF 4. For the circuit shown below, I(t) = 100 cos(103t + 15), R = 10Ω, L1 = 5mH, L2, L3 = 10mH and C = 100µF 1 L1 2 2 I1 L2 R1 I(t) 2 1 L3 C1 1 What is the RMS value of I(t)? IRMS = _______________ What is the phasor representation of the current source? Is = __________________ What is the phasor current through R1 ? IR1= ___________________ What is the phasor voltage across the capacitor Vc Vc = __________________ 5. Consider the circuit shown below. I(t) = 40 cos(100t) A C2 V1 V2 500 uF 2 I2 I(t) R2 40 R3 10 L4 0.2 H 1 Write a simplified node equation for the V1 node. (_________________) V1 + (________________) V2 = ___________ Write a simplified node equation for the V2 node. (___________) V1 + (_________) V2 = ___________ Solve for the phasor voltages(magnitude and phase) V1 = ____________ V2 = ____________ 6. For the circuit below, load A consumes 5kW at a 80% leading power factor. Load B consumes 10 kW at 90% lagging power factor. The voltage source provides 5kVRMS. 5KV (rms) A B Draw the power triangle for Load A. Label the power angle and all sides with magnitude and sign. Load A Draw the power triangle for Load B. Label the power angle and all sides with magnitude and sign. Load B Draw the power triangle for the Source. Label the power angle and all sides with Source magnitude and sign. 7. The input signal Vin(t) = 1 1 1 1 + cos(1000πt ) + cos(3000πt ) + cos(5000πt ) 2 π 3π 5π is applied to the input of a system with a transfer function shown graphically below. H(f) Vin(t) Vout(t) |H(f)| /_H(f) 2 0 -45 -90 1000 2000 3000 f (Hz) 1000 2000 3000 f (Hz) Looking at the magnitude graph of H (f), what kind of ideal filter is represented? |H(f)| represents an ideal _____________ filter. Write a time domain expression for Vout(t) Vout(t) = ____________________________________ 8. Given the cascaded system shown below, assume that the loading effects of the second filter have been accounted for and that all phasors have a common frequency. H1(f) Vin H2(f) Vout If Vin = 15/_ 0 , H1(f) = 3/_-25 , and H2(f) = 10/_ +15, write an expression for the phasor output of the cascaded system Vout . Vout = ____________________ Using the values of H1(f) = 3/_-25 , and H2(f) = 10/_ +15, what is the magnitude of H1(f) and H2(f) in decibels? | H1(f)|dB = __________dB 9. In the circuit below, R = | H2(f)|dB = ___________dB 500 Ω and C= 2µF. 2π What is the transfer function? ________________________ At what frequency, in Hertz, will the amplitude of the output signal, Vout(t) = fb = ___________Hz R Vin(cos wt) Determine the phase angle for Vout at f = fb? C Vout _________________ Vin 2