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648. Standard Resistances.-Standard resistances are made of wire having a small temperature coefficient and not otherwise subject to change. The best coils are made of manganin. The coil is provided with heavy copper terminals of almost negligible resistance, and is so mounted that it will quickly take the temperature of the oil bath in which it is immersed, and by which its temperature is maintained constant.

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649. Resistance Boxes.-Boxes of coils having different resistances are made so as to be conveniently used in measurements, as shown in figure 366. On the hard-rubber top of the box are mounted a number of blocks of brass which can be connected by brass plugs fitting between them. Within the box are the resistance coils wound on spools, one end of a coil being soldered to one block and the other end to the next one so that one coil bridges each gap. The external circuit is connected at the terminal binding screws, and when all the plugs are in, the only resistance is that of the brass blocks and plugs themselves. But if a plug is pulled out the current must then flow through the coil joining the blocks, and accordingly that resistance is introduced.

650. Rheostats.-Coils of wire so mounted that they can easily be thrown into or out of a circuit to regulate the strength of current without particular reference to measurement are known as rheostats. A convenient form is shown in figure 367 where, as the radial arm is moved around the dial from block to block, one coil after another is added to the circuit until as many as may be desired are thrown in.

651. Wheatstone's Bridge.-If a current from a battery E (Fig. 368) divides between the two conductors ACB and ADB, the resistances of these branches may be very different and con

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sequently the current in one may be much larger than in the other, but as they both start at the same point A and end together at B, the fall in potential must be the same in each, and corresponding to any point, such as C in the one, there must be a point D in the other where the potential is the same.

If p, q, r, s are the resistances of the four segments AC, CB, AD, DB then it may be shown that p:q::r: s.

2

Let I, be the current in the upper branch and I, that in the lower branch, then I,p is the drop in potential from A to C and is equal to Ir the drop from A to D,

so also

thus

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652. Slide Wire Bridge.-The relation just demonstrated is made use of in the comparison of resistances, a convenient

device for the purpose being the slide wire bridge shown in figure 369.

Suppose p is some coil of wire whose resistance is to be measured by comparison with a standard resistance box q. The current from the battery E divides at A, part flowing through the branch ACB which consists of the two resistances to be compared, p and q, connected by thick copper strips of extremely small resistance, while part flows through the branch ADB which is a uniform wire

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there is no deflection of the galvanometer, showing that C and D are at the same potential. Then by the previous paragraph the resistance of p must be to that of q as the resistance of r is to that of s, where r and s are the segments of the bridge wire on each side of D. But since the wire is uniform the resistances of r and s are in the same ratio as their lengths, so that the resistance of p is to that of q as the length of r is to the length of s, and therefore p may be calculated by proportion when q is known.

The resistances of the heavy copper connecting strips are so small compared with the resistances of p and q that they may ordinarily be neglected.

653. Platinum Resistance Thermometer.-The increase in resistance in a coil of platinum wire when its temperature is raised has been used by Callendar in the accurate measurement of temperature.

Problems.

1. An electric car line has a resistance of 0.4 ohm per mile. What is the drop in potential in the line if a car 3 miles from the station is using 50 ampères?

2. If one car one mile from station and another two miles from the station are each using 50 ampères, what is the drop in potential to the more distant car, resistance being as in preceding problem? 3. What external resistance when joined to a gravity cell having a resistance of 2 ohms will make the potential difference between the terminals of the cell 0.7 of its electromotive force?

4. A gravity cell of resistance 2 ohms and E. M. F. 1 volt, a dry cell having a resistance of 0.5 ohm and E. M. F. 1.4 volts and a wire of resistance 2.3 ohms are joined in series. Find the drop in potential due to resistance in each part of the circuit, also the potential dif ference between the terminals of each cell.

5. If the cells in the preceding problem are reversed so that one acts against the other, find the drop in potential in each cell and in the external resistance and the potential differences as before.

6. When a current of 31 ampères divides between three parallel conductors whose resistances are 2, 3, and 5 ohms, respectively find the current in each branch, also the drop in potential in the parallel combination.

7. What is the resistance of two conductors connected in parallel, one of 3 and the other of 10 ohms resistance?

8. What part of the whole current will flow through a galvanometer having a resistance of 5 ohms if shunted by a wire of 0.1 ohm resistance?

9. The bridge wire in a slide wire bridge has a resistance of 0.20 ohm; find the current through the wire and also through the resistances, when the resistances compared are 4 and 5 ohms respectively, a dry cell being used having a resistance of 0.3 ohm and E. M. F. 1.4 volts.

ENERGY AND HEATING EFFECT OF CURRENT.

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654. Energy of a Current.-When a current flows from a point where the potential is V, to another point where it is V, each unit charge that passes has less energy at the lower potential than at the higher, and the difference between the two must be the energy which in some form or other is spent between the two points; it may be in heat in the conductor, or in chemical action, or in doing mechanical work. When unit charge passes from V1 to V2 (Fig. 370) the work expended is V1-V2 (§556). If Qunits pass in t seconds the work is

1

2

w=Q(V1— V2)

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But

t

equals I, the current, and the potential difference V1- V2

is represented by P.

1

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Or, the energy spent per second in any part of a circuit is the product of the current strength by the fall in potential in that part.

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If the current and potentials are measured in C. G. S. units then the product will give the energy spent in ergs per second. When the current is in ampères and the potentials are in volts the energy per second is given in units called watts.* From the relations between the ampère and volt and the C. G. S. system (§734) it is seen that one watt = 107 ergs per second.

Thus a watt represents a certain rate of spending energy per second, it is therefore a unit of power, and bears a definite ratio to other units of power.

1 Horse power=746 watts=550 foot-lbs. per second.

655. Where Energy is Absorbed and Where Given Out.From the diagram (Fig. 370) it is seen that everywhere in the external circuit from C to Z the current flows from points of

*The watt is named in recognition of the researches of James Watt on the power of engines.

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