get the equivalent inductance at terminal in

Question

Get the equivalent inductance at terminal in circuit:

Acquire the equivalent inductance at terminal AB in circuit shown in Figure.

Solution

Inductances also follow the same rule as the resistances for series, parallel and star- delta connections. Primary we convert the star connection a b c n to corresponding delta connection.

For delta connection,

L_ab = L_an L_bn + L_bn L_cn + L_cn L_an / L_cn

= 1 + 1 + 1 /1 = 3H

Likewise, L_bc = 3 H and L_ac = 3 H

So, the circuit of Figure is redrawn as illustrated in Figures (a) and (b).

L _eq       = 3/2 H is in parallel with 3 Henry.

 So,

L_eq  = 1.5 × 3 /1.5 + 3 = 1 Henry