2021 Solution 10

Isaac P Abraham
2020 Dec 25

A galvanometer with a resistance R is used to measure the current from a thermocouple of voltage

E

and internal resistance

r

, where

r<<R

. During a physics experiment, the galvanometer needle went off-scale. A bright physicist recalled the concept of current division and recommended adding a resistor

R

in parallel with the ammeter. Current division should cause half the current to flow in the galvanometer, bringing it back in-scale by some amount. How did the galvanometer respond?

Current in the original circuit is,

I

1

=

E

r+R

(

1

)

After shunting the galvanometer the current in the galvanometer is one half the total current in the circuit.

I

2

=

1

2

E

r+

R

2

(

2

)

We are given that

r<<R

. With this in mind, we can simplify (1) and (2).

I

1

|

r<<R

=

E

R

(

3

)

I

2

|

r<<R

=

E

R

(

4

)

Shunting the galvanometer has no effect on the problem of full scale reading.

Ref: Valerii Ilyushchenko (translated by V.N. Lange), "Science for everyone", Mir Publishers, Moscow, USSR.