A potentiometer is a device to precisely measure potential differences or emf, using a “null” technique. In the simple potentiometer circuit shown in Fig. 26–83, R′ represents the total resistance of the resistor from A to B (which could be a long uniform “slide” wire), whereas R represents the resistance of only the part from A to the movable contact at C. When the unknown emf to be measured, Eₓ , is placed into the circuit as shown, the movable contact C is moved until the galvanometer G gives a null reading (i.e., zero) when the switch S is closed. The resistance between A and C for this situation we call Rₓ . Next, a standard emf, Eₛ, which is known precisely, is inserted into the circuit in place of Eₓ and again the contact C is moved until zero current flows through the galvanometer when the switch S is closed. The resistance between A and C now is called Rₛ. Show that the unknown emf is given by
Eₓ = (Rₓ / Rₛ) Eₛ
where Rₓ, Rₛ and Eₛ are all precisely known. The working battery (at top of circuit diagram), as well as the standard cell Eₛ, are assumed to be fresh and to give a constant voltage.
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