# Meter Bridge

It is an electrical device used to find the resistance of the object. It can also compare the resistance of two wires.

Working principle: Meter bridge work in the principle of Wheatstone bridge. In the balanced condition,

$$\frac{\text{P}}{\text{Q}} = \frac{\text{X}}{\text{R}}$$

It consists of one meter long resistive wire fitted on a wooden board. A meter scale is fitted on the wooden board along the length of the wire. On the board, there is a metal strip fitted parallel to the wire. The strip has two gaps, left gap and right gap. In left gap, unknown resistance X is connected and in right gap, a variable resistance R is connected. A cell is connected across the wire along the key as shown in figure. A galvanometer is connected between the point D and jockey.

Working: On closing the key (k), we move the jockey along the wire. Suppose, a galvanometer gives null deflection at point B. Let resistance R_{AB} = P and R_{BC} = Q.

We know, Resistance is proportional to length.

So, P ∝ l_{AB}

and, R ∝ l_{BC}

$\text{or, }\frac{\text{P}}{\text{Q}} = \frac{l_\text{AB}}{l_\text{BC}}$

Let l_{AB} = l m

Then, l_{BC} = (100-l)cm

$\therefore \frac{\text{P}}{\text{Q}} = \frac{ \text{l}}{\text{100-l}}$

$\text{ so, X } = \frac{\text{(100-l)R}}{\text{l}}$

From this relation, we can find the value of unknown resistance.

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