Fig. 18.43 shows a schematic circuit of an instrument called a potentiometer, which is a device for determining very accurate emf values of power supplies. It consists of three batteries, an ammeter, several resistors, and a uniform wire that can be “tapped” for a specific fraction of its total resistance. is the emf of a working battery, designates a battery with a precisely known emf, and designates a battery whose emf is unknown. The switch S is thrown toward battery 1, and the point T (for “tapped”) is moved along the resistor until the ammeter reads zero. Let’s call the resistance of this arrangement R1. This procedure is repeated with the switch thrown toward battery 2, and the point T is moved to T until the ammeter again reads zero. Let’s designate the resistance of this arrangement as R2. Show that the unknown emf can be determined from the following relationship:
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