Two inductors A and B when connected in parallel are equivalent to a single inductor of inductance 1 . 5   H , and when connected in series are equivalent to a single inductor of inductance 8   H . Find the difference in the inductances of A and B .

Question

Two inductors A and B when connected in parallel are equivalent to a single inductor of inductance 1 . 5 &#160; H , and when connected in series are equivalent to a single inductor of inductance 8 &#160; H . Find the difference in the inductances of A and B .

Aicharya · Accepted Answer

When inductors are connected in parallel,

$\frac{1}{1.5} = \frac{1}{L_{1}} + \frac{1}{L_{2}} \dots (1)$

When inductors are connected in series,

$8 = L_{1} + L_{2} \Rightarrow L_{1} = 8 - L_{2} \dots (2)$

Putting the result of equation (2) in (1),

$\frac{1}{1.5} = \frac{1}{8 - L_{2}} + \frac{1}{L_{2}} {L_{2}}^{2} - 8 L_{2} + 12 = 0 L_{2} = 6 H or 2 H and L_{1} = 2 H or 6 H$

Thus difference between the two inductance value is $|6 - 2| = 4$

Two inductors A and B when connected in parallel are equivalent to a single inductor of inductance 1 . 5…

Solution