Physics Part 46

(2) _Unit of quant.i.ty, coulomb._

(3) _Unit of current, ampere._

(4) _Unit of resistance, ohm._

(5) _Unit of electromotive force, volt._

Exercises

1. How will the resistance of 20 ft. of No. 22 German silver wire compare with that of 10 ft. of No. 22 copper wire? Explain.

2. Where in a circuit is copper wire desirable? Where should German silver wire be used?

3. Explain the action of the ammeter. Why does not the needle or coil swing the full distance with a small current?

4. Why is a telegraph sounder more apt to work on a short line than upon a long one?

[Ill.u.s.tration: FIG. 250.--The ammeter is connected in series and the voltmeter in shunt.]

5. Find the resistance of 15 miles of copper telephone wire No. 12. (See table p. 296.)

6. What will be the weight and resistance of 1,000 feet of No. 20 copper wire?

7. A storage battery sends 4 amperes of current through a plating solution. How much silver will it deposit in 2 hours?

8. (a) Compare the diameters of No. 22 and No. 16 copper wire.

(b) Compare the lengths of the same wires giving 1 ohm resistance.

(c) What relation exists between (a) and (b)?

9. Why is an electric bell circuit usually open while a telegraph line circuit is usually closed?

10. A copper wire and an iron wire of the same length are found to have the same resistance. Which is thicker? Why?

11. Why are electric bells usually arranged in parallel instead of in series?

12. What would happen if a voltmeter were put in series in a line?

(3) OHM'S LAW AND ELECTRICAL CIRCUITS

=271. Conditions Affecting Current Flow.=--Sometimes over a long circuit one cell will not work a telegraph sounder. In such a case, two, three, or more cells are connected so that the zinc of one is joined to the copper plate of the other. When connected in this way the cells are said to be _in series_ (Fig. 251). In the figure _A_ represents a voltmeter.

It is found that _when cells are in series the E.M.F. of the battery is the sum of the electromotive forces of the cells_. An ammeter in the circuit shows increased current as the cells are added. Hence _if the resistance of the circuit remains unchanged, the greater the E.M.F. the greater is the current strength_. In this respect, the movement of electricity in a circuit is similar to the flow of water in a small pipe under pressure, as in the latter the flow of water increases as the pressure becomes greater. The current in a circuit may also be increased by lessening the resistance, since the current through a long wire is less than that through a short one, just as the flow of water will be greater through a short pipe than through a long one. To increase the current flowing in an electric circuit, one may therefore either increase the E.M.F. or decrease the resistance.

[Ill.u.s.tration: FIG. 251.--Diagram of cells connected in series.]

=272. Ohm's Law.=--The relation between the electromotive force applied to a circuit, its resistance, and the current produced was discovered in 1827 by George Ohm. Ohm's law, one of the most important laws of electricity, states that, in any circuit, _the current in amperes equals the electromotive force in volts divided by the resistance in ohms_.

This principle is usually expressed thus:

Current intensity = electromotive force/resistance or

Amperes = volts/ohms or _I_ = _E_/_R_

[Ill.u.s.tration: FIG. 252.--The street cars are connected in parallel with each other.]

=273. Resistance of Conductors in Series.=--A study of the _resistance_ of conductors when alone and when grouped in various ways is of importance _since, the current flow through any circuit is dependent upon its resistance_. The two most common methods of combining several conductors in a circuit are in _series_ and in _parallel_. Conductors are in _series_ when all of the current pa.s.ses through each of the conductors in turn (Fig. 218), thus the cell, push-b.u.t.ton, wires, and electric bell in an electric-bell circuit are in series. Conductors are in _parallel_ when they are so connected that they are side by side and a part of the whole current goes through each. None of the current that pa.s.ses through one conductor can go through the conductors in parallel with it. Thus the electric street cars are in _parallel_ with each other. (See Fig. 252.) It is easily seen that none of the current pa.s.sing through one car can go through any of the others. When the conductors are in _series_ the combined resistance is the _sum_ of the several resistances. Thus in an electric-bell circuit if the battery has a resistance of 1 ohm, the bell of 2 ohms, and the wire 1 ohm, the total resistance in the circuit is 4 ohms. When conductors are in _parallel_ the combined resistance is always _less_ than the separate resistances.

Just as a crowd of people meets less resistance in leaving a building through several exits, so electricity finds less resistance in moving from one point to another along several parallel lines, than along one of the lines.

=274. Resistance of Conductors in Parallel.=--If three conductors of equal resistance are in parallel, the combined resistance is just one-third the resistance of each separately (Fig. 253). The rule that states the relation between the combined resistance of conductors in parallel and the separate resistances is as follows:_The combined resistance of conductors in parallel is the reciprocal of the sum of the reciprocals of the several resistances_. For example, find the combined resistance of three unequal resistances in parallel; the first being 4 ohms, the second, 6 ohms, and third 3 ohms. The reciprocals of the three resistances are 1/4, 1/6, and 1/3. Their sum equals 6/24 + 4/24 + 8/24 = 18/24. The reciprocal of this is 24/18 which equals 1-1/3 ohms, the combined resistance.

FIG. 253.--The three conductors are connected in parallel.

This rule may be understood better if we consider the _conductance_ of the conductors in parallel. Since the conductance of a two ohm wire is just one-half that of a one-ohm wire, we say that the conductance of a body is inversely as the resistance, or that it is the _reciprocal of the resistance_. The conductance of the 4-, 6-, and 3-ohm coils will therefore be respectively 1/4, 1/6, and 1/3, and since the combined conductance is the sum of the several conductances, the total conductance is 18/24. Also since this is the reciprocal of the total resistance, the latter is 24/18 or 1-1/3 ohms.

When two or more conductors are connected in parallel each one is said to be a _shunt_ of the others. Many circuits are connected in _shunt_ or in parallel. Fig. 254 represents four lamps in parallel. Incandescent lamps in buildings are usually connected in parallel, while arc lamps are usually connected in series. Fig. 255 represents four lamps in series.

Important Topics

1. Conditions affecting current flow, (a) E.M.F., (b) resistance.

2. Ohm's law, three forms for formula.

3. Resistance of conductors: (a) in series, (b) in parallel; how computed, ill.u.s.trations.

[Ill.u.s.tration: FIG. 254.--The four lamps are connected in parallel.]

[Ill.u.s.tration: FIG. 255.--The four lamps are connected in series.]

Exercises

1. What current flows through a circuit if its E.M.F. is 110 volts and the resistance is 220 ohms?

2. A circuit contains four conductors in series with resistances of 10, 15, 6, and 9 ohms respectively. What current will flow through this circuit at 110 volts pressure? What will be the resistance of these four conductors in parallel?

3. What is the combined resistance of 8 conductors in parallel if each is 220 ohms? What current will flow through these 8 conductors at 110 volts pressure?

4. What is the resistance of a circuit carrying 22 amperes, if the E.M.F. is 20 volts?

5. What E.M.F. will send 8 amperes of current through a circuit of 75 ohms resistance?

6. How does the voltmeter differ from the ammeter?

7. How can one determine the resistance of a conductor?