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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 resistances 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 is terms of $l_{1}, l_{2}$ and S.

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Solution

a) The principle of working of Metre bridge is wheat stone bridge principle and it is used to find the resistance of an unknown conductor or to compare two unknown resistance
b) In meter bridge balance condition is given by
$\frac{R}{S} = \frac{l_{1}}{100 - l_{1}}$
$R = \frac{S l_{1}}{100 - l_{1}}$
When X is connected in parallel with S equivalent resistance in that arm.
$S_{e q} = \frac{S X}{S + X}$
New balanced condition is given by
$\frac{R}{S_{e q}} = \frac{l_{2}}{100 - l_{2}}$
Substituting $R = \frac{S l_{1}}{100 - l_{1}}$
$\frac{S l_{1}}{100 - l_{1}} \times \frac{S + X}{S X} = \frac{l_{2}}{100 - l_{2}}$
Solving this we get,
$(100 - l_{2}) l_{1} (S + X) = (100 - l_{1}) l_{2} X$
$X = \frac{l_{1} S (100 - l_{2})}{100 (l_{2} - l_{1})}$

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