The time constant of L-R circuit is

Step-by-step solution

The instantaneous current in L-R circuit during growth is given by I=I₀ (1-e^ - R_t L ) Since, all the exponential terms are dimensionless, therefore, it follows that factor R L t should be dimensionless i.e. R L t= [ M ^0 ~L ^0 ~T ^0 ] array ll & R L = [ M ^0 ~L ^0 ~T ^0 ] [ T ] = [ T ⁻¹ ] & [ L R ]=[ T ] array Hence, the time constant of L-R circuit is [ L R ] .