Answer:
The time constant becomes twice.
Explanation:
[tex]T[/tex] = Time constant of the L-R circuit
[tex]L[/tex] = Inductance of the inductor
[tex]R[/tex] = Resistance of the resistor
Time constant of the L-R circuit is given as
[tex]T = \frac{L}{R}\\[/tex]
[tex]T_{1}[/tex] = initial time constant of the L-R circuit = [tex]T[/tex]
[tex]T_{2}[/tex] = final time constant of the L-R circuit
[tex]L_{1}[/tex] = Initial inductance of the inductor = [tex]L[/tex]
[tex]L_{2}[/tex] = Initial inductance of the inductor = [tex]2L[/tex]
For the same resistance, the time constant depend directly on the inductance, hence
[tex]\frac{T_{1}}{T_{2}} = \frac{L_{1}}{L_{2}}\\\frac{T}{T_{2}} = \frac{L}{2L}\\\frac{T}{T_{2}} = \frac{1}{2}\\T_{2} = 2T[/tex]
