Units & Dimensions

JEE Main level, single correct, medium

91 of 149

Question 91 of 149

If L,CL,C and RR are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?

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Answer: (D) LC\dfrac{L}{C}

Dimensions of L is [ML2T−2A−2]\left[M{L}^{2}{T}^{-2}{A}^{-2}\right]
Dimensions of C is [M−1L−2T4A2]\left[{M}^{-1}{L}^{-2}{T}^{4}{A}^{2}\right]
And dimensions of R is [ML2T−3A−2]\left[M{L}^{2}{T}^{-3}{A}^{-2}\right]
Clearly, dimensions of LC=[T]\sqrt{LC}=\left[T\right],
Dimensions of LR=[T]\dfrac{L}{R}=\left[T\right],
Dimensions of CR=[T]CR=\left[T\right] and
Dimensions of LC=[ML2T−2A−2][M−1L−2T4A2]=[M2L4T−6A−4]=R2\dfrac{L}{C}=\dfrac{\left[M{L}^{2}{T}^{-2}{A}^{-2}\right]}{\left[{M}^{-1}{L}^{-2}{T}^{4}{A}^{2}\right]}=\left[{M}^{2}{L}^{4}{T}^{-6}{A}^{-4}\right]={R}^{2}

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