The Measurement of Resistance: Wheatstone bridge Method Objectives To become familiar with the basic principle and operation of the Wheatstone bridge of measuring resistors. Equipment . Slide-wire Wheatstone bridge Galvanometer - Standard decade resistance box - Single-pole, single-throw switch The magnitude of a resistance can be measured by measuring the voltage drop AV across a resistance in a circuit with a voltmeter and the current I through the resistance with an ammeter. By Omh's law, then, R = K. 1 However, the ratio of the measured voltage and current does not give an exact value of the resistance because of the resistances of the meters. This problem is eliminated when compares a resistance with a standard resistance in a Wheatstone bridge circuit [named after the British physicist Sir Charles Wheatstone (1802 1875)]. In this experiment, the Wheatstone bridge method of measuring resistances will investigated. The bridge circuit consists of four resistors, a battery or voltage source, and a sensitive galvanometer. The values of R1, R2, and Rs are all known, and Rx is the unknown resistance (Fig.1) Switch S is closed, and the bridge is balanced by adjusting the resistances R; and R2 until the galvanometer shows no deection (indicating no current ow through the galvanometer branch). As a result, the Wheatstone bridge is called a \"null\" instrument. Assume that the Wheatstone bridge is balanced, so that the galvanometer registers no current. Then points 27 and c in the circuit are at the same potential; current 12 ows through both R: and Rx, and current 11 ows through both R1 and R2. The voltage drop Vde across R5 is equal to the voltage drop across R1, 16:5, for a zero galvanometer deection: Vde = Vfc (1) Similarly, Vbd = Vfa (2) Therefore, from Ohm's law, I I1R1 2 Istt (3) and 37 (4) I1 R2 = 12 RX R-st bor And stoletrod do 12 12 G R2 I1 Fig. 1 Slide-wire Wheatstone bridge. (a) Circuit C RI a diagram for resistance measurements. (b) The LI L2 contact slides over the wire on a meter stick. S (a) (b) ad Wax Then, dividing (3) by the (4) and solving for Rx R2 Rest (5) R1 Hence, when the bridge is balanced, the unknown resistance Rx can be found in terms of the standard resistance Rs and the ratio R2/R1. The condition (5) of the balance does not depend on either the battery electo motive force or its internal resistance and voltages and currents do not enter in a direct way in this measurement. The line from a to c represents a wire, and b is a contact key that slides along the wire so as to divide the wire into different-length segments, the resistance of the two sections are proportional to the lengths. If resistance per unit length is r, then from (5) gives RX = 12 R = =2 Rust L1 L1 (6) This type of bridge is convenient since the length segments can be measured easily. The resistances R, and Rz of the length segments may be quite small relative to Rx and R because the bridge equation depends only on the ratio -. This fact makes it possible to use a wire as one side of the bridge