Two inductances connected in parallel are equivalent to a single inductance of 1.5 H and when connected in series are equivalent to a single inductance of 8 H. The difference in their inductance is:

Question

Two inductances connected in parallel are equivalent to a single inductance of 1.5 H and when connected in series are equivalent to a single inductance of 8 H. The difference in their inductance is: (A) 3 H (B) 7.5 H (C) 2 H (D) 4 H

Tardigrade Admin · Accepted Answer

∴ In parallel, Lp=(L1 L2/L1+L2) ( L 1+ L 2) 1.5= L 1 L 2 and in series, LS=L1+L2=8 ∴ L 1 L 2=12 (L1-L2)2=(L1+L2)2-4 L1 L2 L D =√(6)2-4 × 12 L D =4 H

Q. Two inductances connected in parallel are equivalent to a single inductance of $1.5 H$ and when connected in series are equivalent to a single inductance of $8 H$ . The difference in their inductance is:

$3 H$

$7.5 H$

$2 H$

$4 H$

$∴$ In parallel, $L_{p} = \frac{L _{1} L _{2}}{L _{1} + L _{2}}$
$(L_{1} + L_{2}) 1.5 = L_{1} L_{2}$
and in series, $L_{S} = L_{1} + L_{2} = 8$
$∴ L_{1} L_{2} = 12$
$(L_{1} - L_{2})^{2} = (L_{1} + L_{2})^{2} - 4 L_{1} L_{2}$
$L_{D} = (6)^{2} - 4 \times 12$
$L_{D} = 4 H$

Q. Two inductances connected in parallel are equivalent to a single inductance of 1.5H and when connected in series are equivalent to a single inductance of 8H. The difference in their inductance is:

3H

7.5H

2H

4H