Question

If \( R \) and \( C \) denote resistance and capacitance of a material, then the dimension of \( CR \) will be

• A. [MLT]
• B. [M\(^0\)L\(^0\)T]
• C. [M\(^0\)L\(^0\)T\(^2\)]
• D. [M\(^2\)L\(^0\)T]

Hint:

For dimensional analysis, simply multiply the dimensions of the quantities involved and simplify to find the overall dimension.

Answer 1

The Correct Option is B

The dimensional formula of resistance \( R \) is \( [ML^2T^{-3}A^{-2}] \) and the dimensional formula of capacitance \( C \) is \( [M^{-1}L^{-2}T^4A^2] \). To find the dimension of \( CR \), we multiply the dimensions of \( R \) and \( C \): \[ \text{Dim}(CR) = [ML^2T^{-3}A^{-2}] \times [M^{-1}L^{-2}T^4A^2] = [M^0L^0T^0] \] Thus, the dimension of \( CR \) is \( [M^0L^0T^0] \), which is a dimensionless quantity. Therefore, the correct answer is (B).