A) \[[{{M}^{o}}{{L}^{o}}T{{A}^{o}}]\]
B) \[[M{{L}^{o}}T{{A}^{-2}}]\]
C) \[[M{{L}^{o}}T{{A}^{2}}]\]
D) \[[MLT{{A}^{-2}}]\]
Correct Answer: A
Solution :
For a R-C circuit a time constant is calculated as product of Rand C. \[\therefore \] Dimensions of R C = Dimensions of time\[=[{{M}^{0}}{{L}^{0}}T{{A}^{0}}]\]. Alternative : Dimensions of capacitance C and R are \[C=[{{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{A}^{2}}],\,R=[M{{L}^{2}}{{T}^{-3}}{{A}^{-2}}]\] \[\therefore \] Dimensions of CR \[=[{{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{A}^{2}}]\,[M{{L}^{2}}{{T}^{-3}}{{A}^{-2}}]\] \[=[{{M}^{0}}{{L}^{0}}T{{A}^{0}}]\]
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