2018-12-13 - ELEE2790 - Electric Circuits - Final Exam - A PDF

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This is a midterm for electrical circuits used to help answer....

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ELEE2790U Thursday, December 13th, 2018 8:00 – 11:00 AM

FINAL EXAM A One Aid Sheet – No Calculators

Last Name:________________________________ First Name: _______________________________ Student ID: _______________________________

Please ensure that your name and student number is written on every page.

Make sure to always state any assumptions you make. Marks will not be given for answers which do not contain any work. Note – there are a significant number of bonus marks on this test. Make sure to attempt questions that you feel confident in as fully as you can.

Question

Mark

1 (16) 2 (24) !

3 (20) 4 (20) 5 (20) 6 (20) 7 (20) TOTAL (140)

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018

1. [16 marks] In the questions below, select whether the statement is true or false and justify your answer. (NOTE: No marks will be given for questions where no justification is given.) T/F A The equivalent conductance of a set of parallel resistors is found by adding up the conductances of each of the individual resistors.

B The equivalent impedance of a set of parallel capacitors is found by adding up all of the individual capacitor impedances.

C In a linear circuit with multiple voltage and current sources, the method of source transformations can always be used to convert all of the sources to either only current sources or only voltage sources.

D The methods of node-voltage, mesh current and superposition can always be used with all circuit elements, (both linear and non-linear), to solve for a load voltage.

E Resistors, capacitors and inductors can only dissipate power while voltage and current sources can only supply power.

F A load with a resistor and capacitor in series is connected across a sinusoidal voltage source. It the source changes from a 60 Hz source to a 50Hz source this will decrease the apparent power required by the supply.

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________ G If a sinusoidal voltage source which has a value of vi(t) = sin(45+10t) + cos(6t) is connected to a linear circuit made up of resistors, capacitors and inductors, then the power supplied by this circuit can be found by summing of the power supplied using each of the individual sinusoids from the source.

H A resistor and capacitor in series are “plugged into” an outlet in North America. If the capacitance is relatively small, the circuit will be more efficient if an inductor is placed in parallel because the resulting average power supplied by the outlet decreases.

I

An op-amp with a feedback resistor is able to have an output value vo(t) which is larger than the supply voltage +Vcc.

J

A diode which is connected to a voltage supply which is in series to a resistor will have the identical v-i behavior if the voltage supply is replaced with a current supply and the resistor is moved in parallel to it.

K If a non-linear diode is connected to a linear “black box” circuit, the behavior of this black box circuit becomes non-linear.

L A Bipolar Junction Transistor (BJT) can be modeled using the same linear current dependent current source and a battery for all of it’s operating modes.

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018 2. [24 marks] Short answer questions: a. Describe your two favorite projects at demo day and explain why you chose these. (Do not use your own project as one of these.)

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________ b. The following plot comes from a standard first or second order circuit. Identify: • • • • •

the type of source in the circuit (i.e. voltage source or current source) if the circuit is parallel or series the type of circuit and it’s order (i.e. first order RL or RC, or second order RLC.) the element which is plotted (i.e. is it a resistor, a capacitor or an inductor) BONUS: give reasonable values for all of the circuit elements in the circuit.

Justify your answer.

Source ______________________ Parallel or Series First or Second Order Circuit Type __________________

Element Plotted _______________

Element Values: ____________________________

____________________________

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018 c. You need to build a first order parallel RC circuit, for which the time response must settle to within 5% of it’s final value in about 180 msecs. You have the following components: Resistors: 120kΩ, 15 kΩ,

6 kΩ ,

200 Ω

Capacitors 50 nF, 1 uF,

40 uF,

300 uF

Which components will you use in order to get as close as possible to this settling time? Justify your answer. As part of your answer, sketch the resulting currents through both your resistor and capacitor if the source is a DC current source of 2A which is originally off and is turned on at time t=0.

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________ d. Consider a diode with the following diode v-i characteristics. If the diode is connected to a practical voltage source with vs = 10V, then what range of resistors will guarantee that the circuit has a unique solution (i.e. a unique Q-point)?

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018 e. A 500 Ω resistor and a 3.2uF capacitor in series are “plugged into” an outlet where the electricity standard is 110Vrms at 50Hz. What are the approximate values of the instantaneous power, the average power, the reactive power and the apparent power?

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________ f. For part e, if you can place an inductor in parallel with the outlet, what would the “best” inductor you could place there be? Justify your answer. What is the resulting apparent power?

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018 3. [ 20 marks] Op Amp circuit analysis: a. Consider the standard inverting feedback configuration:

Assuming that this op-amp acts like an ideal op ap then what is vo(t) in terms of vi(t)? Justify your answers. As part of your justification you must show how to calculate the voltage across the feedback resistor.

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________ b. For op amp configuration in part a, • if Rs = 50 kΩ, Rf = 100 kΩ, RL=1 kΩ and • the op-amp has an internal resistance of 100 kΩ between the two input terminals and the internal resistor at the output terminal is 1 kΩ then redraw this circuit using the equivalent dependant source model and solve for vo(t). Leave your answer in terms of β.

c. What is vo/vi if β=1, β=10, β=100 and β=1,000.

d. When using the same resistors, should your answers in parts a and b be the same? Explain your reasoning and compare your actual answers. Justify your answer.

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018 e. Consider the following non-standard configuration op amp circuit. Give values for Kp, K1 and K2 where vo(t) = Kp vp + K1 v1 + K2 v2. Make sure to state all of your assumptions.

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________ f. Given the op amp feedback configuration in part e, if v1=v2=0V and R1=R2=Rp=Rg=Rf=10 kΩ then give an equation for vo(t).

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018 -

EXTRA WORK SPACE – Question 3 –

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________ - EXTRA WORK SPACE – Question 3 –

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018 4. [20 marks] Consider the circuit shown below:

a. Solve for the power dissipated in the resistor between b and c using node-voltage analysis or justify why it is not possible to solve using this method.

b. Solve for the power dissipated in the resistor between b and c using mesh-current analysis or justify why it is not possible to solve using this method.

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________ Student ID: _______________________________ c. Solve for the power dissipated in the resistor between b and c using superposition or justify why it is not possible to solve using this method.

d. Solve for the power dissipated in the resistor between b and c using equivalent source transformations or justify why it is not possible to solve using this method.

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018 e. Should your answers in parts a, b c and d be the same? Justify your answer.

f. Which of the methods from parts a, b, c and d was easiest and why?

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________ - EXTRA WORK SPACE – Question 4 –

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018 5. [20 marks + BONUS] In the following circuit: a. Identify all components that do not either supply or dissipate power when in DC steady state. Make sure to justify your answer. b. Redraw a simplified circuit which illustrates the steady state DC operation. c. Identify the steady state current in each of your circuit branches. d. Find the DC steady state power supplied by each of the sources. e. BONUS: Show that the total power supplied = total power dissipated when in DC steady state.

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________ - EXTRA WORK SPACE – Question 5 –

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018 - EXTRA WORK SPACE – Question 5 –

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________ - EXTRA WORK SPACE – Question 5 –

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018

6. [20 marks] Consider the following circuit.

a. What is the DC steady state voltage vo(t) in terms of vs(t)?

b. Identify the differential equation that governs the time response / dynamics of this circuit? Define vo(t) using your differential equation variables. NOTE: A second order differential equation is equivalent to a system of two first order equations – this is most easily done by using the current in the inductor as one state variable and the voltage is the capacitor as the other state variable.

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________ c. What is the equivalent impedance of the parallel capacitor and inductor branches? Note: You can leave your answer as a ratio of complex numbers.

d. Using your answer in c, extrapolate the DC steady state voltage vo(t) in terms of vs(t)? Does/should your answer match what you got in a? Justify your answer.

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018 e. If vs(t) = 2 sin( 5t ), then what is the steady state signal vo(t)?

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________ - EXTRA WORK SPACE – Question 6 –

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018 7. [20 marks] Using the following circuit, where • vs1(t)=10V is the voltage source in the left branch of the switch, • vs2(t)=5V is the voltage source in the right branch of the switch, and • vo(t) is the output voltage across the 10uF capacitor on the right of the circuit, answer the questions below:

a. What does the switch do in this circuit?.

b. Draw a simplified equivalent circuit for positions 1 and 2.

c. For each switch position, how long would it take any transients in the circuit to die down to within 2% of their steady state value?

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________ d. Sketch the output voltage vo(t) if the switch moves between position 1 and position 2 at a frequency of 4 Hz.

e. If the batteries in vs1(t) and vs2(t) were replaced with sinusoidal voltage sources, what is the equivalent impedance of the circuit when the switch is in position 1?

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018 f. If the switch is in position 1 and vs1(t) = 10 sin ( 5t) and vs2(t) = 10 sin (5t) then what is vo(t)? (Include both the transient and steady state components.)

g. In parts e and f, how does this value change when the switch moves to position 2?

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________ - EXTRA WORK SPACE – Question 7 –

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018 - EXTRA WORK SPACE – Please identify which questions any work on this page belongs to.

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: FINAL EXAM – December 13th, 2018 Last Name:______________________________ First Name: _______________________________ Student ID: _______________________________ - EXTRA WORK SPACE – Please identify which questions any work on this page belongs to.

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UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY ELEE2790U: Final Exam – December 13th, 2018 - EXTRA WORK SPACE – Please identify which questions any work on this page belongs to.

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