Three pure inductors each of inductance $6\text{ H}$ are connected as shown in the figure. Their equivalent inductance between the points 'P' and 'Q' is
Choose the correct answer from the options given below
Show Hint
For $n$ identical components connected in parallel, the equivalent value is simply the individual component value divided by the total number of branches ($R/n$ or $L/n$). Here, we can quickly compute $L_{eq} = \frac{6\text{ H}}{3} = 2\text{ H}$ in one step.
Step 1: The problem.
Three coils (inductors), each of $6$ H, are joined by crossing wires between points P and Q. We need the single inductance that could replace all three.
Step 2: Find how they are connected.
We trace the wires. The crossing wires make one end of every coil touch point P and the other end of every coil touch point Q. So all three coils share the same two points.
Step 3: Name the connection.
When all parts join the same two points, they are in parallel.
Step 4: The parallel rule for inductors.
For inductors in parallel we add the reciprocals:
\[ \frac{1}{L_{eq}} = \frac{1}{L_1} + \frac{1}{L_2} + \frac{1}{L_3} \]
Step 5: Put in the values.
Each coil is $6$ H:
\[ \frac{1}{L_{eq}} = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2} \]
Step 6: Invert to get the answer.
\[ L_{eq} = 2\ \text{H} \]
So the equivalent inductance is $2$ H, which is option (4).
\[ \boxed{L_{eq} = 2\ \text{H}} \]
