Question

If $C$ and $R$ denote capacitance and resistance, the dimensional formula of $CR$ is

• A. $[M^0 L^0 T^1]$
• B. $[M^0 L^0 T^{-1}]$
• C. $[M^0 L^0 T^0]$
• D. not expressible in terms of $M,L\, and T$

Answer 1

Answer: (A)

$[M^0 L^0 T^1]$

Answer 2

Capacitance $C=\frac{\text{charge}}{\text{Potential difference}}$ Dimensions of $C=\frac{[AT]}{[ML^2T^{-3}A^{-1}]}$ $=[M^{-1}L^{-2}T^4A^2]$ Resistance $R=\frac{\text{Potential difference}}{\text{current}}$ $=\frac{ML^2T^{-3}A^{-1}}{[A]}=[ML^2T^{-3}A^{-2}]$ Dimensional formula of $CR$ $=[M^{-1}L^{-2}T^4A^2][ML^2T^{-3}A^{-2}]=[T]$ As the $(CR)$ has dimensions of time and so is called time constant of $CR$ circuit.