COMEDK · Physics · 2. Units and Dimensions
If \(R\) and \(C\) denote resistance and capacitance of a material, then the dimension of \(C R\) will be :
- A \(\left[\mathrm{ML}^0 \mathrm{~T}\right]\)
- B \(\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}\right]\)
- C \(\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^2\right]\)
- D \(\left[\mathrm{M}^2 \mathrm{~L}^0 \mathrm{~T}\right]\)
Answer & Solution
Correct Answer
(B) \(\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}\right]\)
Step-by-step Solution
Detailed explanation
The dimension of resistance \(R\) is given by \(R = \dfrac{V}{I}\). Since \(V = \dfrac{W}{q}\), we have \(R = \dfrac{W}{Iq} = \dfrac{[ML^2T^{-2}]}{[A][AT]} = [ML^2T^{-3}A^{-2}]\). The dimension of capacitance \(C\) is given by \(C = \dfrac{q}{V}\). Since \(V = \dfrac{W}{q}\), we…
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