A) \[\left[ M{{L}^{2}}{{T}^{-2}}{{A}^{-2}} \right]\]
B) \[\left[ M{{L}^{2}}T{{A}^{-2}} \right]\]
C) \[\left[ M{{L}^{2}}{{T}^{-1}}{{A}^{-2}} \right]\]
D) \[\left[ M{{L}^{2}}{{T}^{-2}}{{A}^{-1}} \right]\]
Correct Answer: A
Solution :
emf induced in an electrical circuit \[e=L\frac{dI}{dt}\] (numerically) or \[L=e\frac{dt}{dt}\] \[=\frac{W}{Q}.\frac{dt}{dI}\left( \because e=V=\frac{W}{Q} \right)\] \[=\frac{Wdt}{It.dI}\] \[=\frac{[M{{L}^{2}}{{T}^{-2}}][T]}{[A][T][A]}=[M{{L}^{2}}{{T}^{-2}}{{A}^{-2}}]\]
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