Question 7.12: For the magnetic circuit of Fig. 7.30, find I2 , V2 and V2 /...

Writing the mesh equation for the two meshes, we have

(1 + j10 × 1) $\overline{I}_{1}$ – j10 × 8 $\overline{I}_{2}$ = 10 ∠ 0° (Mesh 1)

(1 + j10) $\overline{I}_{1}$ – j80 $\overline{I}_{2}$ = 10 ∠ 0°                 (i)

– j10 × 8 $\overline{I}_{1}$ + (500 + j10 × 80) $\overline{I}_{2}$ = 0 (Mesh 2)

or                     j80 $\overline{I}_{1}$ – (500 + j800) $\overline{I}_{2}$ = 0                    (ii)

From Eq. (ii), we get

$\overline{I}_{1}$ = [(500 + j800)/(j80)] $\overline{I}_{2}$ = (10 – j6.25) $\overline{I}_{2}$                (iii)

Substituting Eq. (ii) in Eq (i), we get

[(1 + j10) (10 – j 6.25) – j80] $\overline{I}_{2}$ = 10 ∠ 0°

or                        $\overline{I}_{2}$ = 0.135 ∠ – 10.7° A

∴                        $\overline{V}_{2}$ = 500 $\overline{I}_{2}$ = 68 ∠ – 10.7°

∴                        $\overline{V}_{2} /  \overline{V}_{1}$ = 6.8 ∠ – 10.7°