Making Use of the Carey Foster Bridge

Lab Report
Bsc Physics,1st years, Chennai Mathematical Institute

Carey Foster Bridge
Aim :
To determine the resistance per unit length, ρ of the Carey Foster bridge wire and hence to find the resistance of a given wire of unknown low resistance.

Apparatus :
• Carey Foster bridge • Two Equal Resistances • Thick Copper Strip • Fractional Resistance Box • Lead Accumulator • Galvanometer • Unknown Low Resistance • Key • Connecting Wires

Theory :
Circuit diagram for the experiment is shown in following Figure.

-- The standard resistances P, Q. -- Fractional resistance box X. -- Unknown resistance Y. -- A one meter long wire of uniform cross-section EF. -- A lead accumulator with a key K . -- Galvanometer G , Terminal B , Jockey D.

The position of jockey D is adjusted to locate the position where there is no deflection of the galvanometer when the jockey is pressed to make electrical contact with the wire; this position is called the balance point or null point. The bridge has its highest sensitivity when all four of the resistances, P, Q, X and Y, have similar magnitudes as the Carey Foster Bridge effectively works like a Wheatstone’s bridge If the balance point is located at a distance l1 from E, then we can write the condition of balance as : • P/Q = R/S = ( X + α + l1 ρ ) / { Y + β + ( 100 − l1 )ρ } ... eq (1)

where α and β are the end corrections at the left and right ends. These end corrections include the resistances of the metal strips to which the wire is soldered, the contact resistances between the wire and the strips, and they also allow for the non-coincidence of the ends of the wire with the zero and one hundred division marks on the scale. Interchanging position of X & Y and combining with eq (1) and simplifying We get : • Y = X − (l2 − l1)ρ ... eq(2)

where l2 is the new distance of the balance point from E. Once we know l1, l2, ρ and X, the unknown resistance Y can be determined .Clearly balance points will only be possible if...