Question

If $C$ and $R$ denote capacitance and resistance, then dimensions of $CR$ will be

• A. $\left[M^0{L}^{0}T{A}^0\right]$
• B. $\left[M{L}^{0}T{A}^{-2}\right]$
• C. $\left[M{L}^{0}T{A}^2\right]$
• D. $\left[M{L}^0{T}^2{A}^{-2}\right]$

Answer 1

Answer: (A)

$\left[M^0{L}^{0}T{A}^0\right]$

We know that value $RC$ gives time constant in an $R-C$ circuit and that $V\left(t\right)=V_0{e}^{\frac{-t}{RC}}$
Exponents are always dimensionless, thus $\left[\frac{-t}{RC}\right]=M^0{L}^0{T}^0{A}^0$ or $\left[RC\right]=\left[t\right]=\left[M^0{L}^0{T}^1{A}^0\right]$