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GUJCET · Physics · Alternating Current
The dimensional formula of \(j \omega L\) is ____________ . Take \(Q\) as the dimension of charge.
- A \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-1} \mathrm{Q}^{-2}\)
- B \(\mathrm{M}^{-1} \mathrm{~L}^{2} \mathrm{~T}^{-1} \mathrm{Q}^{-2}\)
- C \(\mathrm{M}^{1} \mathrm{~L}^{-2} \mathrm{~T}^{-1} \mathrm{Q}^{-2}\)
- D \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{1} \mathrm{Q}^{-2}\)
Answer & Solution
Correct Answer
(A) \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-1} \mathrm{Q}^{-2}\)
Step-by-step Solution
Detailed explanation
(A) \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-1} \mathrm{Q}^{-2}\)
unit of \(\mathrm{j} \omega \mathrm{L}\) is ohm
\(
\begin{aligned}
\mathrm{R} & =\frac{\mathrm{V}}{\mathrm{I}} \\
& =\frac{\mathrm{W}}{\mathrm{I} t} \times \frac{1}{\mathrm{I}} \\
& =\frac{\mathrm{W}}{\mathrm{Q}} \times \frac{t}{\mathrm{Q}} \\
& =\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-1} \mathrm{Q}^{-2}
\end{aligned}
\)
unit of \(\mathrm{j} \omega \mathrm{L}\) is ohm
\(
\begin{aligned}
\mathrm{R} & =\frac{\mathrm{V}}{\mathrm{I}} \\
& =\frac{\mathrm{W}}{\mathrm{I} t} \times \frac{1}{\mathrm{I}} \\
& =\frac{\mathrm{W}}{\mathrm{Q}} \times \frac{t}{\mathrm{Q}} \\
& =\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-1} \mathrm{Q}^{-2}
\end{aligned}
\)
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