Question

In a meter bridge experiment the resistance of the resistance box is $16\,\Omega $, which is inserted in the right gap. The null point is obtained at $36\,cm$from the left end. The least count of meter scale is $1\,mm.$ The value of unknown resistance is?

Answer 1

Hint:A metre bridge, also known as a sliding wire bridge, is a device that works on the Wheatstone bridge idea. It's used to figure out a conductor's unknown resistance. The experiment below shows how to use a metre bridge to estimate the resistance of a specific wire and the resistivity of its substance.

Complete step by step answer:
A slide wire bridge is another name for a metre bridge equipment. It is made out of a long wire with a uniform cross-sectional area that is fastened to the wooden block. The Wheatstone's bridge is made up of two gaps formed by thick metal strips.
Then, applying Wheatstone's principle, we have:
$\dfrac{X}{R} = \dfrac{l}{{(100 - l)}}$
We can calculate unknown resistance:
$X = R \times \dfrac{l}{{(100 - l)}}$

By using above formula:
$R = $Value of known resistance $ = 16\Omega $
$\Rightarrow l = length = 36\,cm$
For calculating unknown resistance formula:
$X = R \times \dfrac{l}{{(100 - l)}}$
$\Rightarrow X = 16 \times \dfrac{{36}}{{(100 - 36)}}$
$\Rightarrow X = 16 \times \dfrac{{36}}{{64}}$
$\therefore X = 9\Omega $
The accuracy with which a metre bridge can measure the value of current is known as its sensitivity. When all resistances are of the same order, the bridge is most responsive.

Note:Because of its high specific resistance or resistivity, manganin or eureka wire is utilised in metre bridges. Because copper is a good conductor of electricity, thick copper strips are utilised in metre bridges.