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Which of the following options gives the dimensional formula of electrical potential?

Asked in GUJCET 2021 · Units and dimensions

• (1) [M⁻¹L²T⁻³A¹]
• (2) [M⁰L³T³A⁻¹]
• (3) [M⁻¹L⁻²T⁻⁴A²]
• (4) [M¹L²T⁻³A⁻¹]

Step-by-step solution

Why the other options are wrong

• (1) No single slip produces [M⁻¹L²T⁻³A¹] -- it is the answer with the signs on M and A reversed. In V=W/q the work stands in the numerator and the charge in the denominator, which forces M¹ and A⁻¹. Sanity check: (M¹L²T⁻²)/(T¹A¹)=[M¹L²T⁻³A⁻¹].
• (2) [M⁰L³T³A⁻¹] carries no mass at all, so it cannot be an energy per unit charge -- the volt is J C⁻¹ and a joule carries M¹.
• (3) [M⁻¹L⁻²T⁻⁴A²] is one exponent away from capacitance, [M⁻¹L⁻²T⁴A²], which is the partner of potential in C=q/V rather than the potential itself -- and capacitance carries T⁴, not T⁻⁴.

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