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Asked in GSEB Board March 2020 (old course) · Units and dimensions
Given: the voltage sensitivity S_V of a moving-coil instrument.
Idea: it is the deflection produced per unit potential difference, S_V=θ/V, and a deflection in radian is a pure number.
So [S_V]=1/([V]), with [V]=M¹L²T⁻³A⁻¹.
Inverting every exponent: [S_V]=M⁻¹L⁻²T³A¹.
Check through the instrument itself: S_V=θ/(IR)=(NAB)/(kR), and (A⁻¹)/(M¹L²T⁻³A⁻²)=M⁻¹L⁻²T³A¹ -- the same.
So the voltage sensitivity has the dimensions M⁻¹L⁻²T³A¹.
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