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Meter Bridge

a Write the p...

Question

(a) Write the principle of working of a metre bridge.
(b) In a metre bridge, the balance point is found at a distance $l_{1}$ with resistance R and S as shown in the figure.

An unknown resistance X is now connected in parallel to the resistance S and the balance point is found at a distance $l_{2}$ . Obtain a formula for X in terms of $l_{1}, l_{2}$ and S.

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Solution

(a) Meter bridge works on the principle of balanced Wheatstone bridge i.e., when the bridge is balanced,
$\frac{R_{1}}{R_{2}} = \frac{R_{3}}{R_{4}}$
Where $R_{1}, R_{2}, R_{3}$ and $R_{4}$ are the resistances connected in four arms of Wheatstone's bridge.
(b) In first case,
$\frac{R}{S} = \frac{l_{1}}{100 - l_{1}} . . . (i)$
In second case,
$\frac{R}{X S / (X + S)} = \frac{l_{2}}{100 - l_{2}} (i i)$
Dividing (ii) by (i),
$\frac{X + S}{X} = \frac{l_{2}}{l_{1}} (\frac{100 - l_{1}}{100 - l_{2}}) 1 + \frac{S}{X} = \frac{l_{2}}{l_{1}} (\frac{100 - l_{1}}{100 - l_{2}}) X = \frac{S}{\frac{l_{2}}{l_{1}} (\frac{100 - l_{1}}{100 - l_{2}}) - 1} X = \frac{l_{1} (100 - l_{2})}{100 (l_{2} - l_{1})} S$

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