of the electrical pressure developed by the cell, that is, of the P.D. between its unconnected terminals.

The common voltmeter (Fig. 278) is, then, exactly like an ammeter, except that it offers so high a resistance to the passage of electricity through it that it does not appreciably reduce the P.D. between the points to which it is connected. 320. The commercial

voltmeter. In Fig. 279 is shown the principle of construction of the common form of commercial voltmeter. It differs from

B

Β ́

FIG. 279. Principle of commercial
voltmeter

the ammeter (Fig. 269) in that the shunt is omitted, and a high-resistance coil R is put in series with the moving coil c. The resistance of a voltmeter may be many thousand ohms. The current that passes through it is very small.

321. The electromotive forces of galvanic cells. Let a voltmeter of any sort be connected to the terminals of a simple galvanic cell, like that of Fig. 246. Then let the distance between the plates and the amount of their immersion be changed through wide limits. It will be found that the deflection produced is altogether independent of the shape or size of the plates or their distance apart. But if the nature of the plates is changed, the deflection changes. Thus, copper and zinc in dilute sulphuric acid have an E.M.F. of one volt, carbon and zinc show an E.M.F. of at least 1.5 volts, and carbon and copper show an E.M.F. of

very much less than a volt. Similarly, by changing the nature of the liquid in which the plates are immersed, we can produce changes in the deflection of the voltmeter.*

We learn, therefore, that the E.M.F. of a galvanic cell depends simply upon the materials of which the cell is composed, and not at all upon the shape, size, or distance apart of the plates.

322. Fall of potential along a conductor carrying a current. Not only does a P.D. exist between the terminals of a cell on

open circuit, but also between any two points on a conductor through which a current is passing. For example, in the electrical circuit shown in Fig. 280 the potential at the point a is higher than at m, that at m higher than that at n, etc. just as, in the water circuit shown in Fig. 281, the hydrostatic pressure at a is greater than that at m, that at m greater than that at n, etc. The fall in the water pressure

* A vertical lecture-table voltmeter (Fig. 278) and a similar ammeter are desirable for this and some of the following experiments, but homemade highresistance and low-resistance galvanometers, like those described in "Exercises in Laboratory Physics," by Millikan, Gale, and Davis, are thoroughly satisfactory, except for the fact that one student must take the readings for the class.

between m and n (Fig. 281) is measured by the water head n's. If we wish to measure the fall in electrical potential between m and n (Fig. 280), we touch the terminals of a voltmeter to these points in the manner shown in the figure. Its reading gives us at once the P.D. between m and n in volts, provided always that its own current-carrying capacity is so small that it does not appreciably lower the P.D. between the points m and n by being touched across them; that is, provided the current which flows through it is negligible in comparison with that which flows through the conductor which already joins the points m and n.

SUMMARY. The resistance of a conductor varies directly with its length and inversely with its cross-sectional area or square of its diameter.

1' r' s" dꞌꞌ 2

The E.M.F. of any generator is the total electrical pressure it can develop on open circuit.

A magnetic voltmeter is a galvanometer calibrated to give a direct reading in volts.

Voltmeters are attached directly in series with a generator to measure its E.M.F., but are used as a shunt to measure fall in potential (P.D.) in any part of a circuit.

QUESTIONS AND PROBLEMS

1. If 300 ft. of No. 18 copper wire has a resistance of 2 ohms, what is the resistance of 800 ft. of it?

2. The resistance of a certain piece of German-silver wire is 1 ohm. What will be the resistance of another piece of the same length but of twice the diameter ?

3. Consider the diameter of No. 20 wire to be three times that of No. 30. A certain No. 30 wire 1 m. long has a resistance of 6 ohms. What would be the resistance of 4 m. of No. 20 wire made of the same metal?

4. How long a piece of No. 30 copper wire has the same resistance as a meter of No. 30 German-silver wire? (See table of specific resistances, p. 284.)

5. How does the resistance of a tungsten lamp when not lighted compare with its resistance when giving light?

6. If the potential difference between the terminals of a cell on open circuit is to be measured by means of a galvanometer, why must the galvanometer have a high resistance? (See § 319.)

7. In a given circuit the P.D. across the terminals of a resistance of 19 ohms is found to be 3 volts. What is the P.D. across the terminals of a 3-ohm wire in the same circuit?

OHM'S LAW

323. Ohm's law. In 1826 Ohm announced the discovery that the currents furnished by different galvanic cells, or combinations of cells, are always directly proportional to the E.M.F.'s existing in the circuits in which the currents flow, and inversely proportional to the total resistances of these circuits; that is, if I represents the current in amperes, E the E.M.F. in volts, and R the resistance of the circuit in ohms, then Ohm's law as applied to the complete circuit is

As applied to any portion of an electrical circuit, Ohm's

where P.D. represents the difference of potential in volts between any two points in the circuit, and R the resistance in ohms of the conductor connecting these two points. This is one of the most important laws in physics.

Both of the above statements of Ohm's law are included in the equation

Amperes

=

volts ohms

(3)

324. Internal resistance of a galvanic cell. Let the zinc and copper plates of a simple galvanic cell be connected to an ammeter, and the distance between the plates then increased. The deflection of the needle will be found to decrease, or if the amount of immersion is decreased, the current also will decrease.