Question

The time constant of $L-R$ circuit is

• A. $LR$
• B. $\frac{L}{R}$
• C. $\frac{ R }{L}$
• D. $\frac{1}{L R}$

Answer 1

Answer: (B)

The instantaneous current in $L-R$ circuit during growth is given by
$I=I_{0}\left(1-e^{-\frac{R_{t}}{L}}\right)$
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 ]}=\left[ T ^{-1}\right] $
$\Rightarrow \left[\frac{ L }{R}\right]=[ T ]$
Hence, the time constant of $L-R$ circuit is $\left[\frac{L}{R}\right]$.