ECE103 Spring Homework 1

Transcription

1 ECE103 Spring 2015 Homework 1 Due Tuesday January 29 in class. Show all your work; all problems must be properly solved and assumptions justified. A list of results is NOT acceptable. Solve the homework on separate sheets of paper, i.e. not this paper, and preferably on engineering paper. 1- Find the charge and sketch its waveform when the current entering a terminal of an element is as shown in the figure below. Assume that q(t)=0 for t<0. The vertical axis represents the current in A and the horizontal axis time in s Find the charge that has entered the terminal of an element from t = 0 s to t = 3 s when the current entering the element is shown in the figure below. The vertical axis represents the current in A and the horizontal axis time in s

2 3- The figure shows four circuit elements identified by letters A, B, C and D a- Which of the devices supply 12 W of power? b- Which of the devices absorbs 12 W of power? 4- The following figure shows a circuit where all the element currents and voltages are specified. Are these voltages and currents correct? Justify your answer 5- For the circuit shown in the figure, a) determine which components are absorbing power and which are delivering power. b) Is conservation of energy satisfied? Explain your answer

3 6- A lightning bolt carried a current of 20kA and lasted 100ms. The voltage between the clouds and the ground is V. Determine the total charge transmitted to the earth and the energy released 7- A 12V battery requires a total charge 40 Ah during recharging. What energy is supplied to the battery? 8- How much energy does a 10HP motor deliver in 30 minutes? Assume that 1HP (horsepower) equals 746W 9- A 600W TV receiver is turned on for 4 hours with nobody watching it. If electricity costs $0.10/kWh, how much money is wasted? 10- An electroplating bath as shown in the figure is used to plate silver uniformly onto objects like kitchenware. A current of 600 A flows for 20 minutes and each coulomb transports mg of silver. What is the weight of silver deposited in grams?

4 ECE103 Spring 2015 Homework 2 Due Thursday February 5 in class. Show all your work, all problems must be properly solved and assumptions justified. A list of results is NOT acceptable. Solve the homework on separate sheets of paper, preferably engineering paper. Do not solve the homework in this page. 1- A certain device has a voltage difference of 5V across it. If 2A of current is flowing through it from its (-) voltage terminal to its (+) terminal, is the device a power supplier or a power recipient, and how much energy does it supply or receive in 1 hour? 2- For each of the 8 devices in the circuit determine if the device is supplying or receiving power and how much power is supplying or receiving. 3- Given the following circuits find (a) the current I and the power absorbed by the resistor and (b) the voltage across the current source and the power supplied by the source.

5 4- Write KCL equations for each node in the following circuit 5- Using the rules for parallel and series connection simplify the following circuit and determine Vx and the power absorbed in the 8 Ω resistor 6- In the circuit shown in the figure below determine all the indicated currents. Hint: Use parallel and series connection rules to simplify the circuit.

6 ECE103 Spring 2015 Homework 3 Due Thursday February 12 in class. Show all your work; all problems must be properly solved and assumptions justified. A list of results is NOT acceptable. Solve the homework on separate sheets of paper, i.e. not this paper, and preferably on engineering paper. 1- The potentiometer (variable resistor) R x in the figure below is to be designed to adjust the current I x from 5A to 10 A. Calculate the values of R and R x to achieve this 2- Design problem You are designing a Christmas tree light set, to be strung on a tree in your backyard, that will operate from a 6-V battery. The heavy-duty rechargeable battery you selected can provide a continuous 9A of current for a 4-hour period of operation each night before being completely drained. Design a set of lights that are configured in a parallel arrangement that will match the performance specifications of your battery. The resistance of each bulb is 12 Ω. Design for the case of the maximum number of lights. 3- Find the equivalent resistance of the following networks.

7 4- Using nodal analysis solve for the following circuits. 5- The circuit below is Wheatstone bridge. Is used to implement an electronic scale. A strain gauge employing a high sensitivity flexible resistor can measure small deflections caused by weight. As the weight deflects the surface on which the resistor is attached the resistor stretched in length causing its resistance to increase from the nominal value R (no weight) to R+ ΔR. The other three resistors in the circuit are identical and equal to R. Find an approximate expression for V out (the voltage difference between nodes 1 and 2) for ΔR/R<<1.

8 6- The circuit in the figure is used to control a motor such that the motor draws currents 15A,10A and 5A when the switch is in HIGH, MEDIUM and LOW positions respectively. The motor can be modeled as a load resistance of 20 mω. Determine the series resistances R 1, R 2 and R 3.

9 ECE103 Spring 2015 Homework 4 Due Thursday February 26 in class. Show all your work; all problems must be properly solved and assumptions justified. A list of results is NOT acceptable. Solve the homework on separate sheets of paper, i.e. not this paper, and preferably on engineering paper. 1- Apply nodal analysis to determine the current I. Consider that the lower node is ground 2- Apply nodal analysis to determine the voltage Va. Consider that the lower node is ground 3- Apply nodal analysis to determine the current I. Consider that the lower node is ground. 4- Apply mesh analysis to determine I

10 5- Apply mesh analysis to determine I 6- Find V0 using superposition 7- Using source transformation determine the current through and the power dissipated in the 8Ω resistor.

11 ECE103 Spring 2015 Homework 5 Due Thursday March 5 in class. Show all your work; all problems must be properly solved and assumptions justified. A list of results is NOT acceptable. Solve the homework on separate sheets of paper, preferably on engineering paper. Do not use these pages for providing the solutions to the homework problems. 1- Find V0 using source transformation 2- Use source superposition to obtain V0 3- The Thevenin equivalent at terminals A-B of a linear network is to be determined by measurement. When a 5 Ω resistor is connected to the terminals A-B the measured voltage V AB is 5V. When a 15Ω resistor is connected, the measured voltage V AB is 7.5V. Find the Norton equivalent of the linear network. 4- Find the Norton equivalent circuit at terminals (a,b)

12 5- A linear circuit is connected to a variable resistor. An ideal ammeter (with zero internal resistance) and an ideal voltmeter (with infinite internal resistance) are used to measure the voltage and the current as shown in the figure. The results of the measurements are shown in the table. R(Ω) V(V) I(A) What will be the current through the variable resistor when it is set to R=18 Ω? 6- A battery has a short circuit current of 20A and an open circuit voltage of 12V. If the battery is connected to a light bulb of resistance 1.4 Ω, what will be the power dissipated by the bulb?

13 ECE103 Spring 2015 Homework 6 Due Thursday March 12. Show all your work; all problems must be properly solved and assumptions justified. A list of results is NOT acceptable. Solve the homework on separate sheets of paper, preferably on engineering paper. Do not use these pages for providing the solutions to the homework problems. 1- Find the Thevenin equivalent circuit at terminals (a,b). [ Rth=3Ω, Vth=3V] 0.25 v o 6 Ω 2 Ω a 18 V Ω + v o - b 2- Find the value of R for the maximum power transfer. [100Ω] L 3- When connected to a 4Ω resistor, a battery has a terminal voltage of 8 V, but produces a 12V on an open circuit. What is the Thevenin equivalent circuit? [Vth=12V, Rth=2Ω]

14 4- Find the Norton equivalent circuit at terminals (a,b). [I N =6A, R N =20/3Ω] 5- A linear circuit is connected to a variable resistor. An ideal ammeter (with zero internal resistance) and an ideal voltmeter (with infinite internal resistance) are used to measure the voltage and the current as shown in the figure. The results of the measurements are shown in the table. R(Ω) V(V) Calculate the current when R=15 Ω. [I=2/3A] 6- For the circuit in problem 5, find the maximum power that the circuit can deliver. [P max =12W]

15 ECE103 Spring 2015 Due Thursday March 26 in class. Homework 7 1- For the circuit in the figure, find the voltage V0 Annswer: Vo= -2V 2- For the circuit in the figure, if V1=10V and V2=5V, find the output voltage V0 Answer: Vo = -5V 3- For the circuit in Exercise 2, if V1=10V and V2=0, find the current I 0 Answer: Vo=-20V 4- Calculate the voltage ratio V0 V 1 for the op amp in the figure

16 Answer: Vo/V1 = Calculate the voltage V0 in the circuit in the figure Answer : Vo = -10V 6- Calculate the gain Vout/Vin, for the circuit shown below Answer: Vout/Vin = 4/3

17 7- What is Vout over the full range of the potentiometer, i.e. from its minimum value of 0 ohms to it maximum value, for the circuit shown below? Answer : Vout max -10V Vout min -5V 8- What is the overall gain, Vout/Vin, for the circuit shown below? Answer: Vout/ Vin = -1

18 ECE103 Spring 2015 Due Thursday April 2 in class. Homework 8 1- Assign a resistance value to Rf so that the circuit would deliver 75 mw of power to the load resistor R L =3kΩ. Answer: 16 kohm 2- Obtain the expression for the voltage gain G=V 0 /V s for the following circuit Answer: [R L / R 1 ] (R1+R2) / (R3+R L ) 3- Evaluate G=V 0 /V s for the circuit in the figure Answer G=1/3 4- Relate Vo to Vs in the circuit in the figure

19 Answer: Vo = (38-4 V S ) figure 5- Relate Vo to Vs in the circuit of the Vo = - { [R1/ R2] (R1+R2) / (R1 + R S ) } V S 6- Relate Vo to Vs in the circuit of the figure Vo = 8.5 V S

20 ECE103 Spring 2015 Due Thursday April 9 in class. Homework 9 1- Two coaxial cables are connected in parallel and charged to 12 V. If the charge accumulated is 600 pc, what is the capacitance of the parallel cable connection? 2- A 10 µf capacitor has an accumulated charge of 500 nc. Determine the voltage across the capacitor 3- Determine the value of C1 50 pf 50 mv 4 uf 4- Find Ceq 1.5 uf 5- Find the equivalent inductance Leq. All inductors are 6 mh 9.42 mh

21 6- The wavefront for the voltage across the capacitor shown in the figure (a) is given by the figure in (b). Determine the following quantities: a) the energy stored in the capacitor at t = 2.5 ms mj b) the energy stored in the capacitor at t = 5.5 ms 1.25 mj c) the current in the capacitor at t = 1.5 ms 1 A d) the current in the capacitor at t = 4.75 ms 0 A e) the current in the capacitor at t = 7.5 ms 0.5 A 7- The wavefront for the current in the 2 H inductor shown in figure (a) is given in figure (b). Determine: a) The energy stored in the inductor at t = 1.5 ms 0.9 mj b) The energy stored in the inductor at t = 7.5 ms uj c) The voltage in the inductor at t = 1.5 ms 0 d) The voltage in the inductor at t = 2.75 ms - 40 V e) The voltage in the inductor at t = 6.25 ms 15 V

22 ECE103 Spring 2015 Due Thursday April 23. Homework We have experimented a loss of electrical power in our homes. When that happens even for a second, we typically find that we need to reset all our digital alarm clocks. Let us assume that the digital clocks need a current of 1 ma at a typical voltage of 3V, but the hardware will function properly down to 2.4 V. Under these assumptions, we wish to design a circuit that will hold the voltage level for a short duration, for example 1 second. Hint: Use a circuit simila to the figure. Calculate the value of C 2- Design an op-amp circuit in which the relationship between the output voltage V 0 and the two input signals V 1 and V 2 is: V 0 = " # 5 V 1 t ( ) dt ( ) $ % 2V t 2 3- An uncharged capacitor of 1 mf is charged by a constant current of 1 ma. Find the voltage across the capacitor after 4 seconds 4- Find the value of C if the energy stored in the capacitor equals the energy stored in the inductor.

23 ECE103 Spring 2015 Due April 30. Homework The switch in the figure has been closed for long time and it opens at t = 0. Find V(t) for t > 0 2- Calculate the voltage across the capacitor 3- In the circuit in the figure, the switch was in the position A for long time. At t=0 it is switched to position B. The voltage in the capacitor for t > 0 is: 4- For the circuit in problem 3, the switch was in the position B for long time and at t = 0 is switched to position A. The voltage in the capacitor for t > 0 is: 5- The switch in the circuit in the figure has been closed for long time. It opens at t=0. Find i(t) for t > 0.

24 6- The switch in the circuit in the figure has been open for long time. It closes at t=0. Find i(t) for t > 0.

25 ECE103 Spring 2015 Due May 7. Homework Calculate the integral sin ( 2π ) δ( 1) t t dt 2- If Vs changes from 2 V to 4 V at t = 0, we may express Vs as: 2 δ t V a. ( ) 2 ut b. ( ) V 2+ 2ut c. ( ) V 2 d. ( ) + 4 ( ) ut ut V e. None of the above 3- Which one is the right statement? a- ( t) du ( t) δ = dt dr ( t) δ t = dt du ( t) r t = dt ut = rt dt b- ( ) c- ( ) d- ( ) ( ) e- All are wrong 4- Write the following voltage signal as a function of time using singularity functions (unit, impulse, ramp).