2300 ECE CIRCUIT ANALYSIS HOMEWORK #2 Notes a) Power terminology: In class we use the terms "delivered" and "absorbed" to indicate the direction of power flow. For example, the battery in a flashlight "delivers" electrical power to the bulb; the bulb "absorbs" electrical power. Nilsson/Riedel uses various terms: "supplied" is equivalent to "delivered", and "dissipated" is equivalent to "absorbed". They also use the term "developed" (Prob. 2.13) to mean either case, that is, they want you to calculate the power in each circuit element, and find out whether positive power is delivered or absorbed. Then, take the values of the power expressions for positive power absorbed and add these results. Do the same thing for the power expressions for power delivered. These two sums should be equal. Each sum is equal to the power developed in the circuit. b) In class we defined "ideal" voltage and current sources. Real voltage and current sources (the kind you actually buy or build) do not behave like ideal sources. Nilsson/Riedel refers to "practical constant current" and "practical constant voltage" sources to describe the way real sources behave. The data (tables) in Probs. 2.21 and 2.22 are supposed to have been taken on "real" sources, as opposed to "ideal" sources. Part b) of 2.22 asks you to construct a circuit model of the practical current source, which can be modeled as an ideal current source in parallel with a resistor. A practical voltage source can be modeled as an ideal voltage source in series with a resistor. 1. This problem comes from Dr. Shattuck's computer-assisted learning project, which is found Next slide on the engineering domain at \\Laser\UHCourses\Ece2300\Dr_Dave_Project. Note that this directory cannot be accessed from the web; you will need to access it from the Engineering Computer Center (ECC), or from another location that allows you access to the domain folders. When you find the directory, do the following. a) Open the file DPKC_Mod01_Part01_v07.ppt and view the slide show found there. This is best done by putting the presentation in Slide Show Mode: from the menu, click on "Slide Show", and then "View Show". Clicking the mouse or pressing the space bar will take you through the slide show. Based on what you have seen, write one or two sentences to answer the question, "Why bother with Reference Polarities?" Remember that it is unacceptable to copy anything directly from Dr. Dave's slides. You must use your own words in giving this answer. b) Open the file PWA_Mod01_Prob03_v05.ppt and view the slide show found there. Again, this is best done by putting the presentation in Slide Show Mode. You will be directed toward the solution by a series of questions. Answer the questions as they are presented, and write down the solution you arrive at.
2. A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure P2.2. A set of resistors was connected to the terminals of the device, one at a time, and the voltage at the device terminals, vt, was measured in each case. The results are shown in Table P2.2. Then, a 10[] resistor was connected to the terminals of the device. Find the power absorbed by this 10[] resistor, when it is connected to the device terminals.
Table P2.2 vt in [V] R in []
(PWA Problem 4 in Module 1)
5
-3.32 -24.2 -113
Device
3. A device can be modeled using a current source in parallel with a resistor. This device was connected to a 5[V] voltage source, as shown in Figure P2.3a), and a current i5 of 0.93[A] resulted. The same device was then connected to a 4[A] current source as shown in Figure P2.3b), and a voltage v4 of 34[V] resulted. Find the voltage v3 if a 3[] resistor, as shown in Figure P2.3c), is connected to the same device. Device + v4 4[A] -
i5 + 5[V] -
15 20
Figure P2.3a)
Figure P2.3b)
Figure P2.3c)
(PWA Problem 5 in Module 1)
2.2
4. a) b) c)
Use the circuit in Figure P2.4 to solve for the numerical values of the quantities requested. Find vX. Find the power delivered by the iS1 current source. Find the power absorbed by the vS3 voltage source.
vS1 = 3vQ + + vX vS2 = 12[V] +
2[] iQ
3[]
+ 7[] vQ +
iS1 = 560[mS]vX
vS3 = 6[]iQ
4[] vS4 = 15[V] 5[] +
Figure P2.4 5. The device shown in Figure P2.5 can be modeled as a current source in parallel with a resistance. When this device is connected to a 5[mA] current source, so that 5[mA] enters the device at terminal A and leaves at terminal B, then the device delivers 296[mW] to the 5[mA] current source. Then, when the same device is disconnected from the current source and is connected to a 10[V] voltage source, so that there is a 10[V] voltage at terminal B with respect to terminal A, then the device absorbs 16.5[mW]. Find the power absorbed the by device when the device is connected to a 10[k] resistor. iQ A
+ vQ B Figure P2.5 Device
2.3
6. Use the circuit shown in Figure P2.6 to find the indicated quantities. a) Find vX. b) Find the power delivered by the vS4 voltage source. vX + iS1 = 4[A] 9[] 13[] 15[]
iQ
7[] iX
vS2 = 10vX
+
36[]
vS1 = 6[]iQ +
11[]
iS2 = 12[A]
+
-
+
-
vS3 = 5[]iX
vS4 = 7[]iQ
Figure P2.6
7. Use the circuit shown in Figure P2.7 to find the numerical values of the quantities requested. a) Find vX. b) Find the power delivered by the voltage source vS2.
17[k] vS2 = 12[V] A + vS5 = 4vX 8.2[k] + iS2 = 5[mA] 22[k] 33[k] vW + B 4.7[k] + + vS1 = 10[V] 19[k] iS1 = 7[mS]vQ + + 5.6[k] vQ + 6.2[k] vX vS3 = 15[V] 1[k] 15[k]
+ vS6 = 5vW
-
vS4 = 20[V]
Figure P2.7
2.4
8. A device can be modeled by a voltage source in series with a resistance. This device has the relationship between voltage vD and current iD shown in Figure P2.8a, using the reference polarities shown in Figure P2.8b. This relationship holds for all values of vD and iD. When this device is connected to a 12[V] voltage source as shown in Figure P2.8c, find the power absorbed by the device.
iD
iD
A +
7[mA]
Device vD
0 0 5[V] Figure P2.8a
vD
Figure P2.8b B
A Device
+
12[V]
B Figure P2.8c
2.5
9. A device, shown in Figure P2.9, can be modeled by a voltage source in series with a resistance. When a resistor with a resistance of 120[] is connected between terminals a and b of the device, the current iT is equal to 230[mA]. Then, when the 120[] resistor is removed, and a resistance of 160[] is connected between terminals a and b of the device, the current iT is equal to 570[mA]. Find iT when the 120[] resistor and the 160[] resistor are removed, and a 200[] resistor is connected between terminals a and b of the device.
Device
iT a
Figure P2.9 b
+ vT -
10. A device, shown in Figure P2.10a, can be modeled by a current source in parallel with a resistance. The relationship between the current through the device, iX, and the voltage across the device, vX, is given in the plot in Figure P2.10b. a) Find a model for the device that would be valid when current is in the range 1[mA] < iX < 5[mA]. This model must have numerical values for the current and resistance, and the polarities with respect to vX and iX should be shown in a diagram. b) A voltage source is applied across the device so that vX = 10[V]. Find the power delivered by the device in this situation.
iX, in [mA]
6
iX + vX Device
5
1 5 6 11
vX, in [V]
Figure P2.10a
Figure P2.10b
11. A device can be modeled as a current source in parallel with a resistance. When this device is connected to a 10[V] voltage source, the voltage source absorbs 4.5[mW]. When the 10[V] voltage source is connected in the opposite polarity to the same device, the voltage source absorbs 65[mW]. Find the power absorbed by the device when it is removed from the voltage source, and connected to a 5.6[k] resistor.
2.6
12. (bonus problem) Four unprepared hikers are returning late from their day hike, at the Redshirt Camp Planning Retreat in the mountains. It is pitch black on a moonless night and they are standing at the edge of a rickety old bridge, which they must cross to return to the retreat house. The bridge crosses a deep canyon and it is so old that it could collapse if more than two people get on the bridge at once. Because it is extremely dark and the bridge is missing planks, it is crucial that the flashlight be used to get across the bridge. The flashlight doesn't have especially strong batteries and the hikers don't want to wait until morning to cross the bridge. The wolves are howling, the bears are hungry, the temperature is dropping, and the dean is waiting impatiently. Each hiker walks at a different pace. Betty is the quickest walker and it will take her a minute to cross the bridge. Dave is the slowest, and didn't even do the full day hike. It will take Dave ten minutes to cross. Kathy can get across in two minutes, and Fritz will amble across in five minutes. No one is willing to risk tossing the flashlight back and forth across the bridge and losing it, so the flashlight has to be carried for each trip. When any two hikers walk together, they must walk at the slower hiker's pace with the flashlight, to ensure that no one trips and stumbles into the deep canyon below. It is impossible to see without the flashlight, and feeling their way across is too risky. How can all the hikers cross the bridge in the quickest time? Find the fastest time that everyone can get across safely.
2.7
Numerical Solutions 1. Solution given in Dr. Dave module. 2. pABS,10// = 8.851 [W] 3. v3 = -0.6481 [V] 4. a) vX = -6.40[V], b) 59.1[W], c) -48.4[W] 5. Solution omitted 6. a) -4.65[V], b) 198[W] 7. a) -4.30[V], b) 479[mW] 8. -286[mW] 9. -1.18[A] 10. a) Solution not given here, diagram required. b) -2[mW] 11. pABS BY DEV = -57.6[mW] 12. Solution omitted
2.8