Manipal Entrance Test 2015 Physics Paper

The instantaneous current in L-R circuit during growth is given
I=I0(1−e−

R

L

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

R

L

t should be dimensionless i.e.

R

L

t=[M0L0T0]
⇒

R

L

=[M0L0T0][T]=[T−1]
⇒[

L

R

]=[T]
Hence, the time constant of L-R circuit is [

L

R

].