Physical World Units and Measurements - Result Question 24
26. Which of the following will have the dimensions of time
(a) LC
(b) $\frac{R}{L}$
(c) $\frac{L}{R}$
(d) $\frac{C}{L}$
[1996]
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Answer:
Correct Answer: 26. (c)
Solution:
(c) $\begin{aligned} \varepsilon & =-L \frac{d i}{d t} \\ \varepsilon & =i R\end{aligned}$
From (1) & (2), $i R=-L \frac{d i}{d t}$
$\therefore \quad$ Dimension of L.H.S. $=$ Dimension of R.H.S.
$[A] R=L[AT^{-1}] \Rightarrow \frac{L}{R}=[T]$
$\frac{L}{R}$ is time constant of R-L circuit so, dimensions of $\frac{L}{R}$ is same as that of time.
