Time constant of an R-L circuit is given by 

Explanation:

An L-R Series Circuit consists basically of an inductor of inductance L, connected in series with a resistor of resistance R. The resistance “R” is the resistive value of the wire turns or loops that go into making up the inductors coil.

Time constant (τ) –

The time constant is defined as the time required for the circuit to reach 63.2% of the final value (steady-state value).

Additional Information

Derivation for Time constant for RL Circuit:

 Consider series RL circuit,

Applying KVL to the circuit,

\(\large{V=Ri(t)+L\frac{di(t)}{dt}}\)

Taking Laplace Transformation of the equation at both sides,

\(\large{\frac{V}{s}=L[sI(s)-i(0+)]+RI(s)}\)

i(0+) = 0 (Since the current just after the switch is on, the current through the inductor will be zero.)

\(\large{\frac{V}{s}=LsI(s)+RI(s)}\)

\(\large{I(s)=\frac{V}{L} \frac{1}{s(s+R/L)}}\)

Now taking Inverse Laplace Transform to the above equation,

\(\large{i(t)=\frac{V}{R}[1-e^{\frac{-Rt}{L}}]=\frac{V}{R}[1-e^{\frac{-t}{T}}]}\)

Where, \(\large{T=\frac{L}{R}}\)

In the RL circuit, at t = T sec, the current becomes 63.2% of its final steady-state value.