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The dimensional formula of capacitance is ________. Take Q as the dimension of charge.

Asked in GUJCET 2017 · Units and dimensions

• (1) M¹L⁻²T⁻²Q⁻²
• (2) M¹L²T⁻²Q⁻²
• (3) M¹L⁻²T²Q²
• (4) M⁻¹L⁻²T²Q²

Step-by-step solution

Why the other options are wrong

• (1) No single slip produces M¹L⁻²T⁻²Q⁻² -- both the mass and the time exponents carry the wrong sign. Sanity check: C=(Q²)/W with [W]=M¹L²T⁻² fixes it at M⁻¹L⁻²T²Q².
• (2) M¹L²T⁻²Q⁻² is exactly 1/C: it comes from writing C=V/Q instead of C=Q/V.
• (3) M¹L⁻²T²Q² is the answer with the mass exponent left positive. In C=(Q²)/W the mass sits in the denominator, so it must come out as M⁻¹.

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