Question

The dimensional formula for RC is:

• A. $[ML^2T^{-3}A^{-2}]$
• B. $[M^0L^0T^{1}A^0]$
• C. $[M^{-1}L^{-2}T^4A^2]$
• D. $[M^0L^0T^0A^1]$

Answer 1

The Correct Option is B

The dimensional formula for \(RC\), where \(R\) is resistance and \(C\) is capacitance, is derived by first establishing their individual dimensional formulas. Resistance \(R\) is defined as \(R = V/I\), with \(V\) representing voltage and \(I\) representing current. The dimensional formula for voltage \(V\) is \([ML^2T^{-3}A^{-1}]\), and for current \(I\) is \([A]\). Consequently, the dimensional formula for resistance \(R\) is:

\[ [R] = [ML^2T^{-3}A^{-1}]/[A] = [ML^2T^{-3}A^{-2}] \]

Capacitance \(C\) is defined as \(C = Q/V\), where \(Q\) is charge and \(V\) is voltage. Given that the dimensional formula for charge \(Q\) is \([AT]\), the dimensional formula for capacitance \(C\) is:

\[ [C] = [AT]/[ML^2T^{-3}A^{-1}] = [M^{-1}L^{-2}T^4A^2] \]

The product \(RC\) is calculated by multiplying the dimensional formulas of \(R\) and \(C\):

\[ [RC] = [ML^2T^{-3}A^{-2}] \times [M^{-1}L^{-2}T^4A^2] \]

Upon simplification, the result is:

\[ [RC] = [M^{1-1}L^{2-2}T^{-3+4}A^{-2+2}] = [M^0L^0T^1A^0] \]

Therefore, the dimensional formula for \(RC\) simplifies to \([M^0L^0T^1A^0]\).