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In a metre bridge experiment null point is obtained at 40cm from one end of the wire when resistance X is balanced against another resistance Y. If X < Y, then the new position of the null point from the same end, if one decides to balance a resistance of 3X against Y, will be close to.
a. $80cm$
b. $75cm$
c. $67cm$
d. $50cm$

Answer
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Hint: A meter bridge is an instrument that works on the wheatstone bridge principle. It is used to find the unknown resistance of the conductor. Find the relation between the two resistance $X$ and $Y$ with the formula where $l$ is the balanced length. Then find the new balanced length when resistance is replaced with $3X$.

Complete step by step answer:
To measure an electrical resistance, a meter bridge is used which is not known by balancing its two legs of the bridge, where one of the legs includes an unknown component.
A meter bridge is an instrument that works on the wheatstone bridge principle. It is used to find the unknown resistance of the conductor.
Meter bridge consists of a wire which is one meter long which has uniform resistance and it has two slots in which one resistance is unknown.
A high resistance is connected in series with the galvanometer to protect it from high currents.The galvanometer is connected between the two resistors.

Jockey one end is connected to the junction of two resistors and the other end is used to find the balancing length. Meter bridge,galvanometer, one meter wire, jockey are used to find the unknown length.
A null point is obtained at point 40cm from one end $X$ then we can write,
$ \Rightarrow \dfrac{X}{l} = \dfrac{Y}{{100 - l}}$
$ \Rightarrow \dfrac{X}{{40}} = \dfrac{Y}{{60}}$
Since $\left( {100 - 40 = 60} \right)$
$ \Rightarrow \dfrac{{3X}}{2} = Y$
Now the new position of the null point then
$ \Rightarrow \dfrac{R}{S} = \dfrac{l}{{l - 100}}$
$ \Rightarrow \dfrac{{6k}}{l} = \dfrac{{3k}}{{100 - l}}$
$ \Rightarrow l = 67$

Hence, the correct answer is option (C).

Note: If a semiconductor is placed in the left gap of a meter bridge and it is heated then, balancing length is shifted to the right. A meter bridge is an instrument that works on the wheatstone bridge principle. It is also used to compare the two resistors. It is also used to determine the specific resistance of a resistor.