COMEDK 2024 Shift 1 Paper

To determine the fraction of the main current passing through the galvanometer and the shunt, we can use the concept of parallel resistances, since both the galvanometer and shunt are connected in parallel in an ammeter.
Let's denote:
Rg as the resistance of the galvanometer, which is 90Ω
Rs as the resistance of the shunt, which is 10Ω
Ig as the current passing through the galvanometer
Is as the current passing through the shunt
I as the main current passing through the ammeter
According to the parallel circuit rule, the voltage across both the galvanometer and shunt will be the same. So, we have:
Rg⋅Ig=Rs⋅Is
Moreover, I=Ig+Is.
First, express Is in terms of Ig :
Is=‌

Rg

Rs

⋅Ig=‌

90

10

⋅Ig=9⋅Ig
Substitute this back into the equation for the total current:
I=Ig+Is=Ig+9⋅Ig=10⋅Ig
Therefore, the fraction of the main current passing through the galvanometer is:
‌

Ig

I

=‌

Ig

10⋅Ig

=‌

1

10

And the fraction of the main current passing through the shunt is:
‌

Is

I

=‌

9⋅Ig

10⋅Ig

=‌

9

10

So, the correct option is:
Option C: ‌

1

10

and ‌

9

10