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Asked in GSEB Board July 2023 · Units and dimensions
Given: the electromotive force ε of a source.
Idea: an emf is the work the source does per unit charge carried round the circuit, ε=W/q -- the same kind of quantity as a potential difference, which is why both are measured in volt.
[W]=M¹L²T⁻² and [q]=[It]=T¹A¹.
[ε]=(M¹L²T⁻²)/(T¹A¹)=[M¹L²T⁻³A⁻¹].
Check by a different route: for an induced emf, ε=-(dΦ)/(dt), so (M¹L²T⁻²A⁻¹)/(T¹) -- the same.
So the dimensional formula of electromotive force is [M¹L²T⁻³A⁻¹].
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