Question

A resistance of 2 is connected across one gap of a metre bridge (the length of the wire is 100 cm) and an unknown resistance greater than 2 is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm . Neglecting any corrections, the unknown resistance is

Answer 1

A resistance of 2 is connected across one gap of a metre bridge (the length of the wire is 100 cm) and an unknown resistance greater than 2 is connected across the other gap. When these resistances are interchanged, the....

Answer 2

Answer:

The value of unknown resistance will be equal to 3Ω connected to second gap of the metre bridge.

Explanation:

Given that the length of the wire=100cm

One resistance =2Ω. and another resistance =x

From the first  given condition:

          $\frac{R}{x} =\frac{I}{100-I}$

         $x=\frac{2(100-I)}{I}$                                      ..................(1)

Second condition:

         $\frac{x}{R} =\frac{I+20}{80-I}$                                            .................(2)

Put the value of x from eq.(1) into Eq.(2)

       $\frac{2(100-I)}{2I} =\frac{I+20}{80-I}$

      $(100-I)(80-I)=I(I+20)$

      $8000-100I-80I+I^{2}=I^{2}+20I$

        $8000=200I$

 ∴        $I=40cm$

Put the value of I in eq. (1)

        $x=\frac{2(40+20)}{80-40}$

        $x=\frac{120}{40}$

∴      $x=3$Ω

Therefore 3Ω is the value of unknown resistance which is connected across the other gap of the metre bridge.