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Let the inductance and resistance be denoted by 'L' and 'R' respectively. The dimensions of $\left(\frac{\mathrm{L}}{\mathrm{R}}\right)$ are
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Verified Answer
The correct answer is:
$\left[\mathrm{L}^{0} \mathrm{M}^{0} \mathrm{~T}^{1}\right]$
We know that;
Dimensional formula of $\mathrm{L}=\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-2}$
Dimensional formula for $\mathrm{R}=\mathrm{R}=\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}$
$\frac{\mathrm{L}}{\mathrm{R}}=\frac{\mathrm{ML}^{2}}{\mathrm{~T}^{2} \mathrm{~A}^{2}} \times \frac{\mathrm{T}^{2} \mathrm{~A}^{2}}{\mathrm{ML}^{2}}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}$
Dimensional formula of $\mathrm{L}=\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-2}$
Dimensional formula for $\mathrm{R}=\mathrm{R}=\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}$
$\frac{\mathrm{L}}{\mathrm{R}}=\frac{\mathrm{ML}^{2}}{\mathrm{~T}^{2} \mathrm{~A}^{2}} \times \frac{\mathrm{T}^{2} \mathrm{~A}^{2}}{\mathrm{ML}^{2}}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}$
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