Question

The resistances in left and right gap of a metrebridge are 20 `Omega` and 30 `Omega` respectively. When the resistance in the left gap is reduced to half its value, the balance point shifts by ______.

Options

• 15 cm to the right.

• 15 cm to the left.

• 20 cm to the right.

• 20 cm to the left.

Answer 1

The resistances in left and right gap of a metrebridge are 20 `Omega` and 30 `Omega` respectively. When the resistance in the left gap is reduced to half its value, the balance point shifts by 15 cm to the left.

Explanation:

`"X"/"R" = l_"x"/l_"R"`

`20/30 =  l_"x"/l_"R"`

`=>  l_"x"/l_"R" = 40/60`  .... (`because l_"x"+l_"R"` =100cm)

`=> l_"x" =  `40 cm

After reducing resistance

`("X"') /"R" = l_"x"^'/(100 - l_"x"^')`

`therefore 10/30 = l_"x"^'/(100 - l_"x"^')`

` l_"x"^' `= 25 cm

The distance through which balance point is shifted `l_"x"-  l_"x"^'` = 40 - 25 = 15 cm to the left.