=277. Illustrative Problems.=--Suppose that four cells are grouped in parallel, each with an E.M.F. of 1.5 volts and an internal resistance of 2 ohms. What current will flow in the circuit if the external resistance is 2.5 ohms? Substitute in the formula for cells in parallel the values given above, and we have _I_ = 1.5/(0.5 + 2.5) = 1.5/3 = 0.5 ampere. Suppose again that these four cells were grouped in series with the same external resistance, substituting the values in the formula for cells in series we have _I_ = 4(1.5)/(4 × 2 + 2.5) = 6/10.5 = 0.57 ampere. =278. Volt-ammeter Method for Finding Resistance.=--Measurements of the resistance of conductors are often made. One of these methods depends upon an application of Ohm's law. It is called the volt-ammeter method since it employs both a voltmeter and an ammeter. If the conductor whose resistance is to be measured is made a part of an electric circuit, being connected _in series with the ammeter_ and _in shunt with the voltmeter_, the resistance may easily be determined, since _R_ = _E/I_. (See Fig. 250.) If, for example, the difference in E.M.F., or as it is often called, the _fall of potential_ between the ends of the wire as read on the voltmeter is 2 volts, and the current is 0.5 ampere, then the resistance of the wire is 4 ohms. This method may be readily applied to find the resistance of any wire that is a part of an electric circuit. =279. The Wheatstone Bridge.=--To find the resistance of a separate wire or of an electrical device another method devised by an Englishman named Wheatstone is commonly employed. This method requires that three known resistances, _a_, _b_, _c_, in addition to the unknown resistance _x_ be taken. These four resistances are arranged in the form of a parallelogram. (See Fig. 259.) A voltaic cell is joined to the parallelogram at the extremities of one diagonal while a moving-coil galvanometer is connected across the extremities of the other diagonal. The known resistances are changed until when on pressing the keys at _E_ and _K_ no current flows through the galvanometer. when this condition is reached, the four resistances form a true proportion, thus _a_: _b_ = _c_: _x_. Since the values of _a_, _b_, and _c_ are known, _x_ is readily computed. Thus if _a_ = 10, _b_ = 100, and _c_ = 1.8 ohms, then _x_, the unknown resistance, equals 18 ohms, since 10: 100 = 1.8: 18. This method devised by Wheatstone may be employed to find the resistance of a great variety of objects. It is the one most commonly employed by scientists and practical electricians. [Illustration: FIG. 259.--Diagram of a Wheatstone bridge.] Important Topics 1. The internal resistance of voltaic cells. 2. Ohm's law applied to groups of cells. (a) Cells in series, (b) cells in parallel. 3. Measurement of resistance: (a) volt-ammeter method, (b) Wheatstone bridge method. Exercises