Question
Mon May 14, 2012 By: Anagha Av

balance condition

Expert Reply
Tue May 15, 2012
 

In this circuit, the ends of a uniform resistance wire R1 are connected to a regulated DC supply VS for use as a voltage divider. The potentiometer is first calibrated by positioning the wiper (arrow) at the spot on the R1 wire that corresponds to the voltage of a standard cell so that 

A standard electrochemical cell is used whose emf is known (e.g. 1.0183 volts for a Weston standard cell).

The supply voltage VS is then adjusted until the galvanometer shows zero, indicating the voltage on R2 is equal to the standard cell voltage.

An unknown DC voltage, in series with the galvanometer, is then connected to the sliding wiper, across a variable-length section R3 of the resistance wire. The wiper is moved until no current flows into or out of the source of unknown voltage, as indicated by the galvanometer in series with the unknown voltage. The voltage across the selected R3 section of wire is then equal to the unknown voltage. All that remains is to calculate the unknown voltage from the fraction of the length of the resistance wire that was connected to the unknown voltage.

The galvanometer does not need to be calibrated, as its only function is to read zero or not zero. When measuring an unknown voltage and the galvanometer reads zero, no current is drawn from the unknown voltage and so the reading is independent of the source's internal resistance, as if by a voltmeter of infinite resistance.

Because the resistance wire can be made very uniform in cross-section and resistivity, and the position of the wiper can be measured easily, this method can be used to measure unknown DC voltages greater than or less than a calibration voltage produced by a standard cell without drawing any current from the standard cell.

If the potentiometer is attached to a constant voltage DC supply such as a lead–acid battery, then a second variable resistor (not shown) can be used to calibrate the potentiometer by varying the current through the R1 resistance wire.

If the length of the R1 resistance wire is AB, where A is the (-) end and B is the (+) end, and the movable wiper is at point X at a distance AX on the R3 portion of the resistance wire when the galvanometer gives a zero reading for an unknown voltage, the distance AX is measured or read from a preprinted scale next to the resistance wire. The unknown voltage can then be calculated: 

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