Units & Dimensions

JEE Main level, single correct, medium

107 of 149

Question 107 of 149

If CC and VV represent capacity and voltage respectively then what are the dimensions of λ\lambda where C/V=λC/V=\lambda ?

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Answer: (A) [M−2L−4I3T7]\left[{M}^{-2}{L}^{-4}{I}^{3}{T}^{7}\right]

λ=CV=Q/VV=QV2\lambda =\dfrac{C}{V}=\dfrac{Q/V}{V}=\dfrac{Q}{{V}^{2}}
V=workQV=\dfrac{work}{Q}
λ=Q3(work)2=(It)3(F.s)2\lambda =\dfrac{{Q}^{3}}{{\left(work\right)}^{2}}=\dfrac{{\left(It\right)}^{3}}{{\left(F.s\right)}^{2}}
=[I3T3][ML2T−2]2=[M−2L−4I3T7]=\dfrac{\left[{I}^{3}{T}^{3}\right]}{{\left[{ML}^{2}{T}^{-2}\right]}^{2}}=\left[{M}^{-2}{L}^{-4}{I}^{3}{T}^{7}\right]

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