## Saturday, July 16, 2011

### Meter Bridge

Meter Bridge
Introduction to Meter Bridge
The working of a Meter Bridge is based on the principle of Wheat stone bridge . It is a simpler form of Wheat stone bridge and is more accurate because , the resistances R and S can be changed in a continuous fashion . It is called a meter bridge it consists of a wire AB of one meter length .
The meter bridge as shown in figure , consists of three thick strips C 1 , C 2 and C 3 made of copper or brass . The resistances of these strips are almost zero . Theshapes and positions of the strips fixed on a wooden board are as shown in figure . A manganin wire of uniform cross section and 1 m length is stretched tight between the two terminals A and B . A jockey J slides over the wire . A graduated meter scale S is fixed by theside of the wire for taking the lengths of the wire . Thelengths are to be measured from th end where +ve terminal of battery is connected i.e. end A in the figure . A battery of emf ' ' , a plug key 'K' are connected between the two terminals A and B . A resistance bax 'RB' is connected in the gap 'G 1 ' . The unknown resistance 'X' is connected in gap 'G 2 ' . In between the centre C of strip C 2 and the jocky 'J' , a galvanometer G and a high resistance 'H.R' are connected in series . When the jockey is at a point 'D' on the wire , it divides the wire into two parts AD and DB of lengths l 1 and l 2 .
As the wire is of uniform cross section , we can haveresistance of AD length of wire =R = l 1 and resistance of DB length of wire = S = l 2 where is the resistance per unit length of the wire . Now , the circuit is exactly similar to a Wheatstone bridge withresistance in RB = P .
Unknown resistance X = Q and R = l 1 and S = l 2 .
When the bridge is balanced, we have
= =
But in a meter bridge l 2 = ( 100 - l 1 ) . So the balanced condition of a meter bridge is =
Experimental Procedure for Meter Bridge
A suitable value of resistance P is kept in the resistance box . In the beginning , the high resistance H.R is included in series with the galvanometer in the circuit . The connections are checked for deflections in galvanometer by pressing the jockey first near A and then at B . If these deflections are in opposite directions , the connections are proper . Otherwise , theconnections are to be checked . The jockey is nowpressed at various points one the wire from 'A' to towards 'B' , until we get near null deflection in the galvanometer . At this stage, the high resistance is shunted and the exact balance point giving null deflection at D is obtained . The length l 1 from A to D is noted . The unknown resistance X can be calculated from equation (1) .
Specific resistance of the material of a given wire can also be determined using meter bridge . We keep the given wire in gap G 2 and determine its resistance (R) as described above . The specific resistance of the material of the wire ( ) is calculated from
=
Precautions
The following precautions are to be observed with a meter bridge experiment .
*. The current must be kept at low value . Otherwise , resistance of wire changeson getting heated and affects the values .
*. The current should not be passed continuously for a very long time . The wire gets heated and values will be altered .
*. The jockey should not be dragged along the wire . Otherwise , the wire gets deformed and its resistance gets altered .
Importance of High Resistance (hr) in Meter Bridge
The galvanometer is a verysensitive current meter . It should be protected from high currents flowing through it . For this reason ,a high resistance is includedin series with the galvanometer . When the balancing point is not obtained , because of H.R in series , the current through galvanometer will be small . But , when the near balance is obtained , the H.R is to be shunted for getting an accurate value for balancing length . Now , there will be no damage to galvanometer , because already near balance is achieved and current through galvanometer will be very small .
Uses
The meter bridge can be conveniently used to
*. determine an unknown resistance
*. compare two resistance
*. determine the specific resistance of the material of a wire .
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