The dimensions of R in the equation $Q = Q_{0} (1 - e^{- t / R C})$ are

[M L^{2} T^{- 3} A^{- 2}]

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[M L^{2} T^{- 2} A^{- 3}]

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[M^{2} L^{2} T^{- 3} A^{- 2}]

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[M L^{2} T^{- 1} A^{- 2}]

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Solution

The correct option is B $[M L^{2} T^{- 3} A^{- 2}]$
$Q = Q_{0} (1 - e^{t / R C})$ . As $t / R C$ is dimensionless.
$∴ R C = t$ or $R = \frac{t}{C}$

$= \frac{t}{Q / V}$

$= \frac{V . t}{Q}$

$R = \frac{[M L^{2} T^{- 2}] [T]}{[A T] [A T]}$

$= [M L^{2} T^{- 3} A^{- 2}]$

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