Question

If $C$ and $R$ denote capacity and resistance, the dimensions of $CR$ are

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

Answer 1

Answer: (A)

In a $CR$ circuit the product $CR$ is the capacitive time constant of the circuit. If $C$ is in farad, $R$ is in ohm, then time constant is in second. Hence, dimensions of $CR=\left[M^0{L}^{0}T\right]$.
Capacitive time constant of $CR$ circuit is the time in which the charge on the capacitor grows from zero to $0.632$ of its maximum value.