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Compare the current sensitivity and volt...

Compare the current sensitivity and voltage sensitivity of the following moving coil galvanometers:
Meters A : `n=30, A=1*5xx10^-3m^2`,
`B=0*25T, R=20Omega`
Meter B: `n=35, A=2*0xx10^-3m^2`,
`B=0*25T, R=30Omega`.
You are given that the springs in the two meters have the same torsional constants.

Text Solution

Verified by Experts

For metre A, `n_1=30`,
`A_1=1*5xx10^-3m^2`, `B_1=0*25T`, `R_1=20Omega`.
For metre B, `n_2=35`, `A_2=2*0xx10^-3m`,
`B_2=0*25T, R_2=30Omega`.
Current sensitity of a meter `=(nBA)/(k)`
`:.("Current sensitivity of meter" A)/("Current sensitivity of meter "B)`
`=(n_1B_1A_1)/(k_1)xx(k_2)/(n_2B_2A_2)=(n_1B_1A_1)/(n_2B_2A_2)`
`(:' k_1=k_2)`
`=(30xx0.25xx1.5xx10^-3)/(35xx0.25xx2.0xx10^-3)=45/70=9/14`
Now voltage sensitivity of a meter`=(nBA)/(kR)`
`:. ("Voltage sensitivity of meter A")/("Voltage sensitivity of meter B")`
`~~` (Ratio of current sensitivity) `xxR_2/R_1`
`=9/14xx30/20xx27/28`
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