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5=6 C=s 3600 s=h 1:87 1022 electrons per hour 1:602 10 19 C=electron
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A typical 12 V auto battery is rated according to ampere-hours. A 70-A h battery, for example, at a discharge rate of 3.5 A has a life of 20 h. (a) Assuming the voltage remains constant, obtain the energy and power delivered in a complete discharge of the preceding batttery. (b) Repeat for a discharge rate of 7.0 A.
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(a) 3:5 A 12 V 42:0 W (or J/s) 42:0 J=s 3600 s=h 20 h 3:02 MJ (b) 7:0 A 12 V 84:0 W 84:0 J=s 3600 s=h 10 h 3:02 MJ
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The ampere-hour rating is a measure of the energy the battery stores; consequently, the energy transferred for total discharge is the same whether it is transferred in 10 hours or 20 hours. Since power is the rate of energy transfer, the power for a 10-hour discharge is twice that in a 20-hour discharge.
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1.8 Obtain the work and power associated with a force of 7:5 10 4 N acting over a distance of 2 meters in an elapsed time of 14 seconds. Ans. 1.5 mJ, 0.107 mW
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Obtain the work and power required to move a 5.0-kg mass up a frictionless plane inclined at an angle of 308 with the horizontal for a distance of 2.0 m along the plane in a time of 3.5 s. Ans. 49.0 J, 14.0 W
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Work equal to 136.0 joules is expended in moving 8:5 1018 electrons between two points in an electric circuit. What potential di erence does this establish between the two points Ans. 100 V
A pulse of electricity measures 305 V, 0.15 A, and lasts 500 ms. What power and energy does this represent Ans. 45.75 W, 22.9 mJ
A unit of power used for electric motors is the horsepower (hp), equal to 746 watts. How much energy does a 5-hp motor deliver in 2 hours Express the answer in MJ. Ans. 26.9 MJ
For t ! 0, q 4:0 10 4 1 e 250t (C).
Obtain the current at t 3 ms.
Ans.
47.2 mA
A certain circuit element has the current and voltage i 10e 5000t A Find the total energy transferred during t ! 0. v 50 1 e 5000t V Ans. 50 mJ
The capacitance of a circuit element is de ned as Q=V, where Q is the magnitude of charge stored in the element and V is the magnitude of the voltage di erence across the element. The SI derived unit of capacitance is the farad (F). Express the farad in terms of the basic units. Ans. 1 F 1 A2 s4 =kg m2
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2.1 PASSIVE AND ACTIVE ELEMENTS An electrical device is represented by a circuit diagram or network constructed from series and parallel arrangements of two-terminal elements. The analysis of the circuit diagram predicts the performance of the actual device. A two-terminal element in general form is shown in Fig. 2-1, with a single device represented by the rectangular symbol and two perfectly conducting leads ending at connecting points A and B. Active elements are voltage or current sources which are able to supply energy to the network. Resistors, inductors, and capacitors are passive elements which take energy from the sources and either convert it to another form or store it in an electric or magnetic eld.
Fig. 2-1
Figure 2-2 illustrates seven basic circuit elements. Elements (a) and (b) are voltage sources and (c) and (d) are current sources. A voltage source that is not a ected by changes in the connected circuit is an independent source, illustrated by the circle in Fig. 2-2(a). A dependent voltage source which changes in some described manner with the conditions on the connected circuit is shown by the diamond-shaped symbol in Fig. 2-2(b). Current sources may also be either independent or dependent and the corresponding symbols are shown in (c) and (d). The three passive circuit elements are shown in Fig. 2-2(e), ( f ), and (g). The circuit diagrams presented here are termed lumped-parameter circuits, since a single element in one location is used to represent a distributed resistance, inductance, or capacitance. For example, a coil consisting of a large number of turns of insulated wire has resistance throughout the entire length of the wire. Nevertheless, a single resistance lumped at one place as in Fig. 2-3(b) or (c) represents the distributed resistance. The inductance is likewise lumped at one place, either in series with the resistance as in (b) or in parallel as in (c). 7
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