Galvanometer Spring Weakness and Current Adjustment

[Jodi]

Hi; Could someone please help me with the following question: If the restoring spring of a galvanometer weakens by 26.4% over the years, what current will give full-scale deflection if it originally required 36.8uA? Thanks for your help.

 

[OlderDan]

Hi; Could someone please help me with the following question: If the restoring spring of a galvanometer weakens by 26.4% over the years, what current will give full-scale deflection if it originally required 36.8uA? Thanks for your help.

You need to make some assumption here about the construction of a galvanometer. I am going to assume you have an ideal case where the angular deflection of the needle is directly proportional to the current because the magnetic field is constructed to achieve that condition, as illustrated here

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/galvan.html

You can then write a direct variation equation that says

Deflection angle = kI

The "weakening of the spring" is saying that k is diminished by 26.4%. So what has to happen to I to achieve the former deflection?

 

[Jodi]

Are you saying to do 0.264 x 36.8E-6? Because that doesn't give me the right answer. Thanks.

 

[OlderDan]

Are you saying to do 0.264 x 36.8E-6? Because that doesn't give me the right answer. Thanks.

No. To have the same deflection angle, the product of k times I must not change. If k is reduced by some fraction, the current is going to have to increase. Let k' and I' be the "new" values for the weakened spring and k and I be the "old" values that gave the same deflection. Then

k'I' = kI

A little bit of algebra from here will get you to the answer.