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The dimensions of R in the equations Q=Q...

The dimensions of R in the equations `Q=Q_(0)(1-e^(-t//RC))` are

A

`[ML^(2)T^(-3)A^(-2)]`

B

`[ML^(2)T^(-2)A^(-3)]`

C

`[M^(2)L^(2)T^(-3)A^(-2)]`

D

`[ML^(2)T^(-1)A^(-2)]`

Text Solution

Verified by Experts

The correct Answer is:
A
`Q=Q_(0)(1-e^(t//RC)`. As `t//RC` is dimensionless
`thereforeRC=t` or `R=(t)/(C)=(t)/(Q//V)=(V.t)/(Q)`
`R=[(ML^(2)T^(-2)])/([AT])([T])/([AT])=[ML^(2)T^(-3)A^(-2)]`
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