Question

If $L$ and $R$ denote inductance and resistance, respectively, then the dimensions of $L/R$ are

• A. $M^1{L}^0{T}^0{Q}^{-1}$
• B. $M^0{L}^{0}T{Q}^0$
• C. $M^0{L}^1{T}^{-1}{Q}^0$
• D. $M^{-1}L{T}^0{Q}^{-1}$

Answer 1

The correct option is B $M^0{L}^{0}T{Q}^0$

We know $E=\frac{1}{2}L{i}^2\Rightarrow L=\frac{2E}{i^2}$

$\Rightarrow$ dimension of $L=\frac{{MLT}^{-2}}{Q^2}.T^2={MLT}^0{Q}^{-2}$

Also we know $E=i^{2}RT\Rightarrow R=\frac{E}{i^{2}t}$

dimension of $R=\frac{{MLT}^{-2}}{Q^2}.T^{-1}={MLT}^{-1}{Q}^{-2}$

$\therefore$ $dim\left(\frac{L}{R}\right)=\frac{{MLT}^0{Q}^{-2}}{{MLT}^{-1}{Q}^{-2}}=\left[T\right]$