Question

In a meter bridge experiment, the value of unknown resistance is $2\Omega $ . To get balancing point at $40\,cm$ distance from the same end, the resistance in the resistance box will be
A. $0.5\Omega $
B. $3\Omega $
C. $20\Omega $
D. $80\Omega $

Answer 1

Hint:By balancing two legs of the bridge circuit, the Wheatstone bridge, also known as the resistance bridge, measures the unknown resistance. One of the legs has an unknown resistance factor. In 1833, Samuel Hunter Christie invented the Wheatstone bridge, which was popularised by Sir Charles Wheatstone in 1843.

Complete step by step answer:
The Wheatstone Bridge Circuit consists of a bridge formed by two known resistors, one unknown resistor, and one variable resistor. This bridge is extremely dependable because it provides precise measurements.The Wheatstone bridge operates on the null deflection principle, which states that their resistance ratios are identical and that no current flows through the circuit.

Under normal circumstances, the bridge is unbalanced, allowing current to pass through the galvanometer. When no current passes through the galvanometer, the bridge is said to be balanced. By changing the known and variable resistances, this condition can be achieved.Now, according to the question; we, know that
$\dfrac{P}{Q} = \dfrac{l}{{100 - l}}$
$ \Rightarrow \dfrac{2}{Q} = \dfrac{{40}}{{100 - 40}}$
$ \Rightarrow \dfrac{2}{Q} = \dfrac{{40}}{{60}}$
$\Rightarrow \dfrac{2}{Q} = \dfrac{2}{3} \\
\Rightarrow 2Q = 6 \\
\therefore Q = \dfrac{6}{2} = 3\Omega $
Therefore, resistance in the resistance box is $3\Omega $.

So, the correct option is B.

Note:The Wheatstone Bridge is used to precisely measure very low resistance values. Temperature, pressure, light, and other physical parameters are measured using a Wheatstone bridge and an active amplifier.