To calculate the Effective Inductance (\(L_e\)):
\[ L_e = \frac{L_1 \cdot L_2}{L_1 + L_2} \]
Where:
Effective inductance refers to the equivalent inductance of two or more inductors when they are connected in parallel. It is a measure of how the inductors combine to influence the overall inductance of the circuit. When inductors are connected in parallel, the total inductance is less than the smallest individual inductance, and the effective inductance can be calculated using the formula provided above. This concept is crucial in designing circuits where specific inductance values are required for proper functionality.
Let's assume the following values:
Using the formula:
\[ L_e = \frac{4 \cdot 6}{4 + 6} = \frac{24}{10} = 2.4 \text{ Henrys} \]
The Effective Inductance is 2.4 Henrys.
Let's assume the following values:
Using the formula:
\[ L_e = \frac{3 \cdot 9}{3 + 9} = \frac{27}{12} = 2.25 \text{ Henrys} \]
The Effective Inductance is 2.25 Henrys.