If 'C' and 'V' represent capacitance and voltage respectively then what are the dimensions of λ where C/V = λ? (a) [M⁻³L⁻⁴I³T⁷] (b) [M⁻²L⁻³I²T⁶] (c) [M⁻²L⁻⁴I³T⁷] (d) [M⁻¹L⁻³I⁻²T⁻⁷]

Answer: (c). [V] = [W/q] = ML²T⁻³I⁻¹. [C] = [q/V] = IT/ML²T⁻³I⁻¹ = M⁻¹L⁻²T⁴I². [λ] = [C/V] = M⁻²L⁻⁴T⁷I³ So the answer is (c) [M⁻²L⁻⁴I³T⁷].

If 'C' and 'V' represent capacitance and voltage respectively then… | JEE Main 2021 (26 Feb, Shift 2)

Q58JEE Main 2021 · 26 FEB · SHIFT 2Easy

Units & Dimensions

If 'C' and 'V' represent capacitance and voltage respectively then what are the dimensions of $\lambda$ where C/V = $\lambda$ ?

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Answer: (c)

$[V] = [W/q] = \mathrm{ML^2T^{-3}I^{-1}}$ .
$[C] = [q/V] = \mathrm{IT}/\mathrm{ML^2T^{-3}I^{-1}} = \mathrm{M^{-1}L^{-2}T^4I^2}$ .
$[\lambda] = [C/V] = \mathrm{M^{-2}L^{-4}T^{7}I^{3}}$
So the answer is (c) $[M^{-2}L^{-4}I^3T^7]$ .