The circuit element shown in Figure P1.15 has v = 15 V and

Broadly speaking, what are the two main objectives of electrical systems?

Name eight subdivisions of electrical engineering.

Briefly describe four important reasons that other engineering students need to learn the fundamentals of electrical engineering.

Write a few paragraphs describing an interesting application of electrical engineering in your field. Consult engineering journals and trade magazines such as the IEEE Spectrum, Automotive Engineering, Chemical Engineering, or Civil Engineering for ideas.

Carefully define or explain each of the following terms in your own words giving units where appropriate: a. Electrical current; b. Voltage; c.An open switch;d.A closed switch; e. Direct current; f. Alternating current.

In the fluid-flow analogy for electrical circuits, what is analogous to: a. a conductor; b. an open switch; c. a resistance; d. a battery?

The ends of a length of wire are labeled a and b. If the current in the wire is iab = 3 A, are electrons moving toward a or b? How much charge passes through a cross section of the wire in 3 seconds?

The net charge through a cross section of a circuit element is given by q(t) = 2t + t 2 C. As usual, t is in seconds. Find the current through the element in amperes.

The current through a given circuit element is given by i(t) = 2et A. As usual, time t is in seconds. Find the net charge that passes through the element in the interval from t = 0 to t = . (Hint:Current is the rate of flow of charge.Thus, to find charge, we must integrate current with respect to time.)

A certain lead-acid storage battery has a mass of 30 kg. Starting from a fully charged state, it can supply 5 A for 24 hours with a terminal voltage of 12 V before it is totally discharged. a. If the energy stored in the fully charged battery is used to lift the battery with 100-percent efficiency, what height is attained? Assume that the acceleration due to gravity is 9.8 m/s2 and is constant with height. b. If the stored energy is used to accelerate the battery with 100 percent efficiency, what velocity is attained? c. Gasoline contains about 4.5 107 J/kg. Compare this with the energy content per unit mass for the fully charged battery.

A typical deep-cycle battery (used for electric trolling motors for fishing boats) is capable of delivering 12.6 V and 10 A for a period of 10 hours. How much charge flows through the battery in this interval? How much energy does the battery deliver?

An ac current given by i (t) = 5sin(200t) A, in which t is in seconds and the angle is in radians, flows through an element of an electrical circuit. a. Sketch i(t) to scale versus time for t ranging from 0 to 15 ms. b. Determine the net charge that passes through the element between t = 0 and t = 10 ms. c. Repeat for the interval from t = 0 to t = 15 ms.

Consider the headlight circuit of Figure 1.2 on page 7. For current to flow through the headlight, should the switch be open or closed? In the fluid-flow analogy for the circuit, would the valve corresponding to the switch be open or closed? What state for a valve, open or closed, is analogous to an open switch?

What is the net number of electrons per second that pass through the cross-section of a wire carrying 5 A of dc current? The current flow is due to electrons, and the magnitude of the charge of each electron is 1.60 1019 C.

The circuit element shown in Figure P1.15 has v = 15 V and i = 3 A.What are the values of vbaand iba? Be sure to give the correct algebraic signs. Is energy being delivered to the element or taken from it? i a b v Figure P1.15

Suppose that the net charge passing through the cross section of a certain circuit element is given by q(t) = 2t + 3t 2 C, with time t in seconds. Determine the current through the element as a function of time.

In typical residential wiring, the copper wire has a diameter of 2.05 mm and carries a maximum current of 15 2 A due solely to electrons, each of which has a charge of 1.60 1019 C. Given that the free electron (these are the electrons capable of moving through the copper) concentration in copper is 1029 electrons/m3, find the average velocity of the electrons in the wire when the maximum current is flowing.

The charge carried by an electron is 1.60 1019 C. Suppose that an electron moves through a voltage of 120 V from the negative polarity to the positive polarity. How much energy is transferred? Does the electron gain or lose energy?

Consider a circuit element, with terminals a and b, that has vab = 12 V and iab = 3 A. Over a period of 2 seconds, how much charge moves through the element? If electrons carry the charge, which terminal do they enter? How much energy is transferred? Is it delivered to the element or taken from it?

What does the term passive reference con- figuration imply? When do we have this configuration if we are using double subscript notation for an element having terminals a and b?

Compute the power for each element shown in Figure P1.21. For each element, state whether energy is being absorbed by the element or supplied by it. ia va + va = 15 V ia = 2 A (a) (b) (c) vDE = 20 V iED = 3 A D E ib vb = 10 V ib = 3 A vb Figure P1.21

A certain battery has terminals labeled a and b. The battery voltage is vab = 12 V. To increase the chemical energy stored in the battery by 600 J, how much charge must move through the battery? Should electrons move from a to b or from b to a?

The terminals of an electrical device are labeled a and b. If vab = 25 V, how much energy is exchanged when a positive charge of 4 C moves through the device from a to b? Is the energy delivered to the device or taken from it?

Consider the element shown in Figure P1.24 which has v(t) = 15 V and i(t) = 3e2t A. Compute the power for the circuit element. Find the energy transferred between t =0 and t = . Is this energy absorbed by the element or supplied by it? i(t) v(t) + Figure P1.24

Suppose that the cost of electrical energy is $0.12 per kilowatt hour and that your electrical bill for 30 days is $60. Assume that the power delivered is constant over the entire 30 days. What is the power in watts? If a voltage of 120V supplies this power, what current flows? Part of your electrical load is a 60-W light that is on continuously. By what percentage can your energy consumption be reduced by turning this light off?

An electrical device has iab(t) = 2 A and vab(t) = 10sin(100t) V, in which the angle is in radians. a. Find the power delivered to the device and sketch it to scale versus time for t ranging from 0 to 30 ms. b. Determine the energy delivered to the device for the interval from t = 0 to t = 10 ms. c. Repeat for the interval from t = 0 to t = 20 ms.

A fully charged deep-cycle leadacid storage battery is rated for 12.6 V and 100 ampere hours. (The ampere-hour rating of the battery is the operating time to discharge the battery multiplied by the current.) This battery is used aboard a sailboat to power the electronics which consume 30 W. Assume that the battery voltage is constant during the discharge. For how many hours can the electronics be operated from the battery without recharging? How much energy in kilowatt hours is initially stored in the battery? If the battery costs $95 and has a life of 250 charge discharge cycles, what is the cost of the energy in dollars per kilowatt hour? Neglect the cost of recharging the battery.

Figure P1.28 shows an ammeter (AM) and voltmeter (VM) connected to measure the current and voltage, respectively, for circuit element A. When current actually enters the + terminal of the ammeter the reading is positive, and when current leaves the + terminal the reading is negative. If the actual voltage polarity is positive at the + terminal of the VM, the reading is positive; otherwise, it is negative. (Actually, for the connection shown, the ammeter reads the sum of the current in element A and the very small current taken by the voltmeter. For purposes of this problem, assume that the current taken by the voltmeter is negligible.) Find the power for element A and state whether energy is being delivered to element A or taken from it if: a. the ammeter reading is +2 A and the voltmeter reading is 25 V; b. the ammeter reading is 2 A and the voltmeter reading is +25 V; c. the ammeter reading is 2 A and the voltmeter reading is 25 V.

Repeat Problem P1.28 with the meters connected as shown in Figure P1.29. + AM + VM A Figure P1.29

Determine the cost per kilowatt hour for the energy delivered by a typical alkaline 9-V transistor battery that costs $1.95 and is capable of delivering a current of 50 mA for a period of 10 hours. (For comparison, the approximate cost of energy purchased from electric utilities in the United States is $0.12 per kilowatt hour.)

Define the term node as it applies in electrical circuits. Identify the nodes in the circuit of Figure P1.31. Keep in mind that all points C D A vA vE B G E F + + + vC + + vB vG vF + vD + Figure P1.31

Use KCL to find the values of ia, ic, and id for the circuit of Figure P1.32. Which elements are connected in series in this circuit? A C D B ia ic id ie = 1 A E ib = 2 A 3 A Figure P1.32

What can you say about the currents through series-connected elements in an electrical circuit?

State Kirchhoffs current law in your own words. Why is it true?

Identify elements that are in series in the circuit of Figure P1.31.

. In the fluid-flow analogy for an electrical circuit, the analog of electrical current is volumetric flow rate with units of cm3/s. For a proper analogy to electrical circuits, must the fluid be compressible or incompressible? Must the walls of the pipes be elastic or inelastic? Explain your answers.

Given that ia = 2 A, ib = 3 A, id = 5 A, and ih = 4 A, determine the values of the other currents in Figure P1.37. B D A id ig ib ia F if C H E ie ih ic G Figure P1.37

Determine the values of the other currents in Figure P1.37, given that ia = 2 A, ic = 3 A, ig = 6 A, and ih = 1 A.

a. Which elements are in series in Figure P1.39? b. What is the relationship between id and ic? c. Given that ia = 6 A and ic = 2 A, determine the values of ib and id . A E B C id ic ia ie i vb b D ve + vc va + + + vd + Figure P1.39

Explain Kirchhoffs voltage law in your own words. Why is it true?

Use KVL and KCL to solve for the labeled currents and voltages in Figure P1.41. Compute the power for each element and show that power is conserved (i.e., the algebraic sum of the powers is zero)

Use KVL to solve for the voltages va, vb, and vc in Figure P1.42. vb + + + + + + 5 V 10 V va 15 V vc Figure P1.42

We know that va = 10 V, vb = 3 V, vf = 12 V, and vh = 5 V, solve for the other voltages shown in Figure P1.43. vd + ve + + va + vf + vb + vg + vc + vh A F B G D E C H Figure P1.43

Consider the circuit shown in Figure P1.31. a. Which elements are in parallel? b. What is the relationship between vA and vC? c. Given that vA = 8 V and vE = 4 V, determine the values of vC and vF .

Identify the elements that are in parallel: a. in Figure P1.32, b. in Figure P1.43.

Identify the nodes in Figure P1.46. Which elements are in series?Which are in parallel? A C B D Figure P1.46

Consider a circuit containing four nodes labeled a, b, c, and d. Also, we know that vab = 12 V, vcb = 4 V, and vda = 8 V. Determine the values of vac and vcd. (Hint: Draw a picture showing the nodes and the known voltages.)

A typical golf cart uses a number of 6-V batteries (which, for the purposes of this problem, can be modeled as ideal 6-V voltage sources). If the motor requires 36 V, what is the minimum number of batteries needed? How should they be connected? Sketch a diagram for the battery connections showing the polarity of each battery.

Explain Ohms law in your own words,including references.

Define these terms in your own words: a. an ideal conductor; b. an ideal voltage source; c. an ideal current source; d. short circuit; e. open circuit.

Name four types of dependent sources and give the units for the gain parameter of each type.

. a. Show that for wires of identical dimensions but made of different materials, such as copper and aluminum, the resistance is proportional to the resistivity of the material. (SeeTable 1.3 on page 28 for resistivity values of some materials used in electrical wiring.) b. We know that the resistance of a certain copper wire is 1.5 . Determine the resistance of an aluminum wire having the same dimensions as the copper wire.

Draw a circuit that contains a 5- resistance, a 10-V independent voltage source, and a 2-A independent current source. Connect all three elements in series. (Because the polarity of the voltage source and reference direction for the current source are not specified, several correct answers are possible.)

Repeat Problem P1.53, placing all three elements in parallel.

Suppose that a certain wire has a resistance of 10 . Find the new resistance: a. if the length of the wire is doubled; b. if the diameter of the wire is doubled.

Suppose we have a copper wire with a resistance of 2 . We want to replace the copper wire with an aluminum wire of the same length and resistance. By what factor must the diameter of the wire be increased?

A power of 100 W is delivered to a certain resistor when the applied voltage is 100 V. Find the resistance. Suppose that the voltage is reduced by 10 percent (to 90 V). By what percentage is the power reduced? Assume that the resistance remains constant.

Sketch the diagram of a circuit that contains a 3- resistor, a 10-V voltage source, and a current-controlled current source having a gain constant of 0.4 A/A. Assume that the current through the resistor is the control current for the controlled source. Place all three elements in parallel. Several answers are possible, depending on the polarities and reference directions chosen.

Sketch the diagram of a circuit that contains a 3- resistor, a 2-A current source, and a voltage-controlled current source having a gain constant of 2 S. Assume that the voltage across the resistor is the control voltage for the controlled source. Place all three elements in parallel. Several answers are possible, depending on the polarities and reference directions chosen.

The current through a 10- resistor is given by i(t)=10exp(2t)A. Determine the energy delivered to the resistor between t = 0 and t = .

The voltage across a 12- resistor is given by v(t) = 24cos(2t) V. Calculate the energy delivered to the resistor between t = 0 and t = 2 s. The argument of the cosine function, 2t, is in radians.

Which of the following are self-contradictory combinations of circuit elements? a. A 12-V voltage source in parallel with a 2-A current source. b. A 2-A current source in series with a 3-A current source. c. A 2-A current source in parallel with a short circuit. d. A 2-A current source in series with an open circuit. e.A 5-V voltage source in parallel with a short circuit.

Consider the circuit shown in Figure P1.63. Use repeated applications of Ohms law, KVL, and KCL to eventually find Vx. + 5 10 5 5 1 A Vx Figure P1.63

Consider the circuit shown in Figure P1.64. Find the current iR flowing through the resistor. Find the power for each element in the circuit. Which elements are absorbing power? 2 A 10 V + iR 5 Figure P1.64

Plot, to scale, iab versus vab for each of the parts of Figure P1.65. 10 V (a) a b + 5 (b) a b 1 A (c) a b 10 4 V (d) a b + 5 1.5 A (e) a b Figure P1.65

Consider the circuit shown in Figure P1.66. a. Which elements are in series? b. Which elements are in parallel? c. Apply Ohms and Kirchhoffs laws to solve for vx.

Given the circuit shown in Figure P1.67, find the power for each source. Which source is absorbing power?Which is delivering power? 12 V 10 A + Figure P1.67

Consider the circuit shown in Figure P1.68. Find the current iR flowing through the resistor. Find the power for each element in the circuit. Which elements are absorbing energy? 4A 12 V 8 iR + Figure P1.68

Use repeated applications of Ohms law, KVL, and KCL to eventually find the value of Ix in the circuit of Figure P1.69. 8 2 4 1 A Ix 2 Figure P1.69

The circuit shown in Figure P1.70 contains a voltage-controlled voltage source. a. Use KVL to write an equation relating the voltages and solve for vx. b. Use Ohms law to find the current ix. c. Find the power for each element in the circuit and verify that power is conserved. 10 V avx + ix 3 + vx + a = 5 V/V Figure P1.70

What type of controlled source is shown in the circuit of Figure P1.71? Solve for vs. + 3 4 2 a = 0.5 S vx vs + avx 1 A Figure P1.71

Consider the circuit shown in Figure P1.72. a. Which elements are in series? b. Which elements are in parallel? c. Apply Ohms and Kirchhoffs laws to solve for Rx. 4 12 V 8 2 Rx 2 A + Figure P1.72

Solve for the currents shown in Figure P1.73.

Figure P1.74 is the electrical model for an electronic megaphone, in which the 16- resistance models a loudspeaker, the source Ix and the 5- resistance represent a microphone, and the remaining elements model an amplifier. What is the name of the type of controlled source shown? Given that the power delivered to the 16- resistance is 16 W, determine the current flowing in the controlled source. Also, determine the value of the microphone current Ix. 5 2 Ix + 16 32

. What type of controlled source appears in the circuit of Figure P1.75? Determine the values of vx and iy. 10 V 12 avx + 2 + vx iy + a = 4 V/V Figure P1.75

A 10-A independent current source is connected in series with a 2- resistance between terminals a and b. What can you say about Problems 43 iab and vab? What single circuit element is equivalent to this series combination?

A 10-V independent voltage source is connected in parallel with a 2- resistance between terminals a and b. What can you say aboutiab and vab?What single circuit element is equivalent to this parallel combination?

Consider the circuit shown in Figure P1.78, given R1 = 15 , R2 = 10 , and Is = 4 A. a. Use KCL to write an equation relating the currents. b. Use Ohms law to write equations relating i1 and i2 to the voltage v. c. Substitute the equations from part (b) into the equation from part (a) and solve for v. d. Find the power for each element in the circuit and verify that power is conserved. Is + v R1 R2 i2 i1 Figure P1.78

Consider the circuit shown in Figure P1.79, given R1 = 3 , R2 = 4 , and Is = 2 A. a. Use KVL to write an equation relating the voltages. b. Use Ohms law to write equations relating v1 and v2 to the current Is. c. Substitute the equations from part (b) into the equation from part (a) and solve for v. d. Find the power for each element in the circuit and verify that power is conserved. R2 R1 Is v1 v v2 + + + Figure P1.79

What types of sources are present in the circuit shown in Figure P1.80? Solve for Is and the voltage v.

KVL is a consequence of KCL and conservation of power in electrical circuits. This problem illustrates this fact for the circuit of Figure P1.81. a. Write the KCL equation for the circuit. b. Apply conservation of power to the circuit, summing the powers for the elements (observing the proper algebraic signs) and setting the sum to zero. c. Use the KCL equation to substitute for i3 in the equation of part (b) and put the result into the form Ai1 + Bi2 = 0, in whichA and B are algebraic sums of the voltages. d. Now, suppose that we have control of the current sources. For any values we select for i1 and i2, the equation of part (c) must be satisfied. This can only happen if we have A = 0 and B = 0. Show that this gives the KVL equations for the circuit. i1 i3 i v4 v5 2 + + v1 + + v2 + v3 Figure P1.81

What types of sources are present in the circuit of Figure P1.82? Solve for the current ix. 24 V aix + ix 5 + a = 3 Figure P1.82