For a series RL circuit, the time constant (\(\tau\)) is given by the formula:
\[ \tau = \frac{L}{R} \]
Where:
L = Inductance in Henries (H)
R = Resistance in Ohms (\(\Omega\))
Given:
Resistance (R) = \(12 \Omega\)
Inductance (L) = 18 H
The DC supply voltage (30 V) is not needed to calculate the time constant itself.
Calculate the time constant:
\[ \tau = \frac{18 \text{ H}}{12 \Omega} = \frac{18}{12} \text{ sec} = \frac{3}{2} \text{ sec} = 1.5 \text{ sec} \]
The time constant is 1.5 seconds.
\[ \boxed{1.5 \text{ sec}} \]