Question

A galvanometer of resistance 30 `Omega` is connected to a battery of emf 2V with 1970 `Omega` resistance in series. A full scale deflection of 20 divisions is obtained in the galvanometer. To reduce the deflection to 10 divisions, the resistance in series required is ____________.

पर्याय

• 4030 `Omega`

• 4000 `Omega`

• 3970 `Omega`

• 2000 `Omega`

Answer 1

A galvanometer of resistance 30 `Omega` is connected to a battery of emf 2V with 1970 `Omega` resistance in series. A full scale deflection of 20 divisions is obtained in the galvanometer. To reduce the deflection to 10 divisions, the resistance in series required is 3970 `Omega`.

Explanation:

`"I" = "V"/(("R" + "r"))`

` = 2/((1970 + 30))`

` = 2/2000`

` = 1  "mA"`

∴ for 10 divisions of deflection,

I = 0.5 mA

`therefore 0.5 xx 10^-3 = 2/(("R" + "r"))`

`therefore "R'" + "r" = 2/(0.5 xx 10^-3)`

`therefore "R'" = (4 xx 10^3) - 30`

`therefore "R'" = 3970  Omega`