ECE3413-01 Test4

Spring 2015

NAME: ___________________________________ NetID ___________________

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Keep this exam booklet

FLAT

INSTRUCTIONS 1. This is a work-at- home exam consisting 10 total questions.

2. You must print out the test as individual pages and work each page. You may not reformat the

test, so that multiple problems are on one page. You must turn in all pages, stapled, but not

folded. You may add additional pages with your work if necessary.

3. Calculators are allowed.

4. Make sure you clearly indicate your answers (i.e., clearly write your answer with units

on the lines provided). Do not just write an answer – you must show your work!

5. This test is due at 8:00 am on Monday, April 13, 2015. No late tests will be accepted.

6. If you have any questions, send an email to me. I will be checking my email regularly.

I will not answer any emails after 10pm on Sunday evening.

1. (10 points) For the circuit shown below, calculate the power for the load. The voltage

source is 𝑣(𝑡) = 120 cos(𝜔𝑡 + 20°) 𝑉 and the current is 𝑖(𝑡) = 10 cos(𝜔𝑡 − 25°) 𝐴 with

the direction shown in the diagram. The frequency is at 60 Hz. Note: Make sure your

answers include units. List any angles in degrees.

Complex Power ______________

Average Power ______________

Reactive Power ______________

Apparent Power ______________

Power Factor ______________

Leading or lagging pf _____________

+

– Load

1. (10 points) The motor inside a blender can be modeled as a resistance in series with an

inductance, as shown. Determine the current pulled by the blender in phasor form, the average power

dissipated in the load, the power factor, and the value of a capacitor when placed in parallel with the

motor which will change the power factor to 0.95 (lagging)? Note: Make sure your answers include

units. List any angles in degrees.

RMS Current ______________________

Pavg dissipated by the load_____________

Power Factor _______________________

Leading or lagging pf ________________

Reactive Power (load) before correction

__________________________________

Size of capacitor ___________________

2. (10 points) Determine the required value of capacitance for perfect pf correction the circuit

below with two loads. Draw the phasor diagram showing the relationship between the two

load currents and the capacitor current. Assume the following values. Assume rms values

for all phasor quantities in this problem.

Vs = 120/0⁰ V; P1 = 500 W; pf1 = 0.7 lagging, P2 = 200 W; pf2 = 0.95 leading; ω= 377 rad/sec.

Load Current (RMS) I1 _________________________

Load Current (RMS) I2 _________________________

Apparent Power |S1| ____________________________

Apparent Power |S2| _____________________________

Reactive Power, Q1 ____________________________

Reactive Power, Q2 ____________________________

Total Reactive Power __________________________

New reactive Power needed for unity pf ___________

Capacitor Size ________________________________

Draw the currents as phasors:

4. (10 points) Given the waveform of the voltage source shown, find:

a) the steady DC voltage (RMS voltage) that would cause the same heating effect across a

resistor.

b) the average current supplied to a 10 Ω resistor connected across the voltage source.

c) The average power supplied to a 1- Ω resistor connected across the voltage source.

VDC = Vrms = ___________________________

Average current for a 10Ω load _____________

Average power for a 1Ω load _______________

5. (10 points) A residential electric power monitoring system rated for 120 Vrms, 60-Hz source

registers power consumption of 1500W, with a power factor of 0.87 leading. Find the

The rms current __________________

The phase angle (how much the current lags the voltage) __________________

The system complex impedance, Z _____________

The system resistance, R _______________

The system reactance, Q _______________

What type of element might generate this reactance ____________________

6. (10 points) A current flows when a neon light advertisement is supplied by a 110 V rms power

system. The current lags the voltage by 40⁰. Find the power dissipated by the circuit and the

power factor. Also determine what size capacitor should be placed in parallel to bring this to

0.90 power factor.

Pavg dissipated by the load_____________

Power Factor _______________________

Capacitor Size ______________________

7. (5 points) The current through a 5 H inductor is given by iL = 2cos (377t +40⁰). Write the

expression for voltage across the inductor in time dependent (standard) form. Box your answer.

Include units.

7b. (5 points) The voltage across a 70-uF capacitor takes the following values. Calculate the

expression for the current through the capacitor in the following case: vc((t) = 10 cos 100t V.

Give your answer in in time dependent (standard) form. . Box your answer. Include units.

8. (10 points) Given v(t) = 150 cos (200πt – 30°) in time dependent or standard form.

Find

angular frequency, ω ______________

Frequency in Hertz _______________

Period __________________________

Peak value______________________

Rms value_______________________

First value of time tmax after t=0 such that v(t) attains positive peak.

______________________________

Draw a picture (labeled) of the sinusoidal voltage.

9.(10 points) Determine the current through Z3 in the circuit of the figure below.

vs1(t) = vs2(t) = 120cos(377t) V Z1=5.9/30⁰ Ω Z2=2.3/15Ω Z3=17/-27⁰ Ω

10. (10 points) Use the definition of complex power to calculate the real and reactive power for

the load shown. Vs = 110/0⁰; Rs = 7 Ω; RL = 15 Ω; jXL = j12 Ω. Determine the power transfer

between source and load. Explain what happens to the remaining power.

Assumptions: Use rms values for all phasor quantities in this problem.