(i) State the principle of working of a meter bridge.
(ii) In a meter bridge balance point is found at a distance l₁ with resistors R and S as shown in the figure.

When an unknown resistor X is connected in parallel with the resistor S, the balance point shift to a distance l₂. Find the expression for X in terms of l₁ l₂ and S.

(i) A slide wire bridge is known as meter bridge. It is constructed on the principle of balanced Wheatstone bridge, when a Wheatstone bridge is balanced then

straight P over straight Q space equals space fraction numerator straight l over denominator 100 minus straight l end fraction

(ii) When resistors R and S are connected. Since balance point is found at a distance l₁from the zero and

therefore

straight R over straight S space equals space fraction numerator straight l subscript 1 over denominator 100 minus straight l subscript 1 end fraction

...(i)
When unknown resistance X is connected in parallel to S.
∴ total resistance in the right hand gap is

straight S subscript 1 space equals space fraction numerator SX over denominator straight S plus straight X end fraction

open square brackets because 1 over straight R space equals space 1 over straight R subscript 1 plus 1 over straight R subscript 2 space space rightwards double arrow space space straight R space equals space fraction numerator straight R subscript 1 straight R subscript 2 over denominator straight R subscript 1 plus straight R subscript 2 end fraction close square brackets

Since the balance point is obtained at a distance l₂ from the zero end

therefore

straight R over straight S subscript 1 space equals space fraction numerator straight l subscript 2 over denominator 100 minus straight l subscript 2 end fraction

putting the value of S₁, we get

fraction numerator straight R over denominator begin display style fraction numerator SX over denominator straight S plus straight X end fraction end style end fraction space equals space fraction numerator straight l subscript 2 over denominator 100 minus straight l subscript 2 end fraction fraction numerator straight R space left parenthesis straight S plus straight X right parenthesis over denominator SX end fraction space equals space fraction numerator straight l subscript 2 over denominator 100 minus straight l subscript 2 end fraction space space space space space space space space space space space space space space space space space space space space... left parenthesis ii right parenthesis

Dividing equation (ii) by (i), we get
(i) A slide wire bridge is known as meter bridge. It is constructed o

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