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If $L$ and $R$ are respectively the inductance and resistance, then the dimensions of $\frac{L}{R}$ will be
Options:
Solution:
1603 Upvotes
Verified Answer
The correct answer is:
$M^0 L^0 T$
We know that;
Dimensional formula of \(\mathrm{L}=\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\)
Dimensional formula for \(\mathrm{R}=\mathrm{R}=\mathrm{ML}^2 \mathrm{~T}^{-3} \mathrm{~A}^{-2}\)
\(\frac{\mathrm{L}}{\mathrm{R}}=\frac{\mathrm{ML}^2}{\mathrm{~T}^2 \mathrm{~A}^2} \times \frac{\mathrm{T}^2 \mathrm{~A}^2}{\mathrm{ML}^2}=\mathrm{M}^{\mathrm{O}} \mathrm{L}^{\mathrm{O}} \mathrm{T}\)
Hence,
option (C) is correct answer.
Dimensional formula of \(\mathrm{L}=\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\)
Dimensional formula for \(\mathrm{R}=\mathrm{R}=\mathrm{ML}^2 \mathrm{~T}^{-3} \mathrm{~A}^{-2}\)
\(\frac{\mathrm{L}}{\mathrm{R}}=\frac{\mathrm{ML}^2}{\mathrm{~T}^2 \mathrm{~A}^2} \times \frac{\mathrm{T}^2 \mathrm{~A}^2}{\mathrm{ML}^2}=\mathrm{M}^{\mathrm{O}} \mathrm{L}^{\mathrm{O}} \mathrm{T}\)
Hence,
option (C) is correct answer.
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