Question

An ammeter is obtained by shunting 'n' `Omega` galvanometer with 'n' `Omega` resistance. The additional shunt required to be connected across it to double the range is ____________.

Options

• n

• `"n"/4`

• `"n"/3`

• `"n"/2`

Answer 1

An ammeter is obtained by shunting 'n' `Omega` galvanometer with 'n' `Omega` resistance. The additional shunt required to be connected across it to double the range is `"n"/2`.

Explanation:

Initially `"S" = "i"_"g"/("I" - "i"_"g") xx "G"`

`"n" = "i"_"g"/("I" - "i"_"g") xx "n"`

`"i"_"g" = "I" - "i"_g Rightarrow "I" = 2"i"_"g"`

`"When the rang is double I'" = 2"I" = 4"i"_"g"`

`"Now, S'" = "i"_"g"/("I'" - "i"_g) "G"`

`= "i"_"g"/(4"i"_"g" - "i"_"g") xx "n"`

`= 1/3 "n"`

Since shunt is connected in parallel, so additional shunt required is

`1/"S'" = 1/"S" + 1/"X"`

`1/"X" = 1/"S'" - 1/"S"`

`3/"n" - 1/"n" = 2/"n"`

`therefore "X'" = "n"/2`