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Two moving coil galvanometer, X and Y ha...

Two moving coil galvanometer, X and Y have coils with resistance `10 Omega and 14 Omega` cross-sertional areas `4.8xx10^(-3)m^(2) and 2.4xx10^(-3)m^(2)`, number of turns 30 and 45 respectively. They are placed in magnetic field of 0.25 T and 0.50 T respectively. Then, the ratio of their voltage sensitivities and the ratiof of their voltage senstivities are respectively

A

`2:3, 14:15`

B

`5:7, 2:1`

C

`2:13, 1:2`

D

`14:15, 2:9`

Text Solution

Verified by Experts

The correct Answer is:
A
There is no information regarding spring constant.
So, let.s assume their spring constants are same. Current sensitivity, `I_(S) =(N BA)/(k)`
So, `(I_(s_(1)))/(I_(s_(2)))=(N_(1)B_(1)A_(1)k_(2))/(N_(2) B_(2) A_(2) k_(1))`
`=(30xx0.25xx4.8xx10^(-3))/(45xx0.5xx24xx10^(-3))xx((1)/(1))`
`(I_(s_(1)))/(I_(s_(2)))=2//3`
Voltage sensitivity, `V_(s) =NBA // Rk`
So, `(V_(s_(1)))/(V_(s_(2)))=(N_(1)B_(1)A_(1)k_(2)R_(2))/(N_(2)B_(2)A_(2)k_(1)R_(1))`
`=(2)/(3) xx((R_(2))/(R_(1)))=(2)/(3)xx(14)/(10)=(14)/(15)`
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