Carey Foster Bridge

Description. The Carey Foster Bridge is a form of Wheat stone’s bridge. It consists of a uniform write AB of length 1 meter stretched on a wooden board.

Two equal resistances P and Q are connected in gaps 2 and 3. The unknown resistance R is connected in gap 1. A standard resistance S, of the same order of resistance as R, is connected in gap 4. A Leclanche cell is connected across MN. A galvanometer G is connecting between the terminal C and a sliding contact maker D.


Theory.  The contact maker is moved until the bridge is balanced. Let I1 be the balancing length as measured from end A. Let α and β be the end resistances at A and B. Let ρ be the resistance per unit length of the wire,
From the principle of Wheat stone’s bridge,
P/Q = R + α + l₁ρ /S + β + (100 = l₁) ρ
The resistances R and S are interchanged and the bridge is again balanced. The balancing length l₂ is determined from the same end A. Then, P/Q = S + α + l₂ρ /R + β + (100 = l₂) ρ _____________... (2)

From Eqns. (1) and (2),
R + α + l₁ρ /S + β + (100 – l₁) ρ = S + α + l₂ρ /R + β + (100 – l₂) ρ _______________________ ... (3)

Adding 1 to both sides of Eq. (3),
R + α + l₁ρ + S + β + 100ρ – l₁ρ /S + β + (100 – l₁) ρ = R+S + α + β + 100ρ – l₂ρ /R + β + (100 – l₂)ρ
. : R + S + α + β + 100ρ /S + β + (100 – l₁) ρ = R + S + α + β + 100ρ /R + β + (100 – l₂) ρ

Since the numerators are equal, the denominators must be equal.
. : S + β + 100ρ = l₁ρ = R + β + 100ρ – l₂ρ ________________________________________  … (4)
Or     S – l₁ρ = R – l₂ρ
        R = S + ρ (l₂ – l₁)________________________________________________________… (5)

 

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