10. The resistance of 1000 ft. of No. 36 copper wire is 424 ohms. How many feet should be used in winding a 200 ohms relay?
11. The resistance of No. 00 trolley wire is 0.80 ohm per 1000 ft. What is the resistance of a line 1 mile long?
12. A wire has a resistance of 20 ohms. It is joined in parallel with another wire of 6 ohms, find their combined resistance.
13. The separate resistances of two incandescent lamps are 200 ohms and 70 ohms. What is their combined resistance when joined in parallel? When joined in series?
(4) Methods of Grouping Cells and Measuring Resistance
275. Internal Resistance of a Voltaic Cell.—The current produced by a voltaic cell is affected by the resistance that the current meets in passing from one plate to another through the liquid of the cell. This is called the internal resistance of the cell. A Daniell cell has several (1-5) ohms internal resistance. The resistance of dry cells varies from less than 0.1 of an ohm when new to several ohms when old. If cells are joined together their combined internal resistance depends upon the method of grouping the cells.
Fig. 256.—The four cans exert four times the water pressure that one can will exert.
276. Cells Grouped in Series and in Parallel.—When in series the copper or carbon plate of one cell is joined to the zinc of another and so on. (See Fig. 251.) The effect of connecting, say four cells, in series may be illustrated by taking four cans of water, placed one above another. (See Fig. 256.) The combined water pressure of the series is the sum of the several pressures of the cans of water, while the opposition offered to the movement of a quantity of water through the group of cans is the sum of the several resistances of the cans. In applying this illustration to the voltaic cell, we make use of Ohm's law. Let E represent the e.m.f. of a single cell, r the internal resistance of the cell, and R the external resistance or the resistance of the rest of the circuit. Consider a group of cells in series. If n represents the number of cells in series, then Ohm's law becomes