Question

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

• A. $\left[ ML ^{0} TA ^{-2}\right]$
• B. $[M^0 L^0 T^{-1}]$
• C. $\left[ M ^{0} L ^{0} TA ^{0}\right]$
• D. not expressible in terms of $M,L\, and T$

Answer 1

Answer: (C)

We know that value $RC$ gives time constant in an $R - C$ circuit and that $V ( t )=$ $V _{0} e ^{\frac{1}{ CC }}$ Exponents are always dimensionless, thus $\left[\frac{-t}{R C}\right]= M ^{0} L ^{0} T ^{0} A ^{0}$ or $[ RC ]=[ t ]=$ $\left[ M ^{0} L ^{0} T ^{1} A ^{0}\right]$