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A galvanometer coil is replaced by anoth...

A galvanometer coil is replaced by another coil of diameter one-fourth of the original diameter and the total number of turns as ten times the original number. What will be the new deflection if the same current is passed through it?

A

`(5)/(8)` times the original deflection

B

`(4)/(5)` times the original deflection

C

`(4)/(3)` times original deflection

D

`(5)/(3)` times original deflection

Text Solution

Verified by Experts

The correct Answer is:
A
Case (I) `A_(1) = (pi D^(2))/(4), n_(1) = n, theta_(1) = theta`
Case (II) `A_(2) = pi ((D)/(8))^(2)`
`A_(1) = (pi D^(2))/(64) n_(2) = 10 n " "theta_(2) = ?`
`I = (Ktheta_(1))/(n_(1)BA_(1)) = (K theta_(2))/(n_(2) BA_(2))`
`theta_(2) = theta_(1) xx (n_(1)A_(1))/(n_(1) A_(1)) = (theta xx 10 n xx (pi D^(2))/(64))/(n xx (nD^(2))/(4))`
`= theta xx 10 xx (1)/(16)`
`theta_(2) = (5)/(8)` times the original
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