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

Question

If C and R denote capacitance and resistance, the dimensional formula of CR is (A) [ ML 0 TA -2] (B) [M0 L0 T-1] (C) [ M 0 L 0 TA 0] (D) not expressible in terms of M,L and T

Tardigrade Admin · Accepted Answer

We know that value RC gives time constant in an R - C circuit and that V ( t )= V 0 e (1/ CC ) Exponents are always dimensionless, thus [(-t/R C)]= M 0 L 0 T 0 A 0 or [ RC ]=[ t ]= [ M 0 L 0 T 1 A 0]

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

$[M L^{0} T A^{- 2}]$

$[M^{0} L^{0} T^{- 1}]$

$[M^{0} L^{0} T A^{0}]$

not expressible in terms of $M, L an d T$

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 $[\frac{- t}{RC}] = M^{0} L^{0} T^{0} A^{0}$ or $[RC] = [t] =$ $[M^{0} L^{0} T^{1} A^{0}]$

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

[ML0TA−2]

[M0L0T−1]

[M0L0TA0]

not expressible in terms of M,LandT