Dimensions of Resistance – Rankers Physics

Dimensions: Practice Problem & Solution

Dimensions of resistance in an electrical circuit, in terms of dimension of mass (M), of length (L), of time (T) and of current (I), would be [2007]
\(ML^2T^{-2}I^{-2}\)
\(ML^2T^{-1}I^{-1}\)
\(ML^2T^{-3}I^{-2}\)
\(ML^2T^{-3}I^{-1}\)

Solution Explained:

To solve this problem, we apply the core principles of Dimensions. Understanding the underlying formula is key to arriving at the correct answer below:

Resistance \(R = V/I = W/(QI)\). (W) is work done, (Q) is charge. \(W = [ML^2T^{-2}]\), \(Q = [IT]\). So, \(R = [ML^2T^{-2}] / ([IT][I]) = [ML^2T^{-3}I^{-2}]\).

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