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Manipal Entrance Test 2015 Physics Paper

Question : 23 of 50

Marks: +1, -0

The time constant of L-R circuit is

Solution:

The instantaneous current in L-R circuit during growth is given

I=I_{0}\left(1-e^{-\frac{R}{L}t}\right)

Since, all the exponential terms are dimensionless, therefore, it follows that factor

\frac{R}{L}t

should be dimensionless i.e.

\frac{R}{L}t=\left[M^{0}L^{0}T^{0}\right]

\Rightarrow \frac{R}{L}=\frac{\left[M^{0}L^{0}T^{0}\right]}{[T]}=[T^{-1}]

\left[\frac{L}{R}\right].

Hence, the time constant of L-R circuit is

\frac{L}{R}

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