λ 

λ 

λ 

λ 

Δ 

λ 

(J1)1  (J1)2  (J1)3 

(IC)1 = 30A 

€

n1n2

1

=15

€

n1n2

2

=15

€

n1n2

3

= 30

ISARE 

(IC)2 = 90A  (IC)3 = 60A 

(IC)1= 30A 

€

n1n2

1

=15

€

n1n2

2

=15⇒ n1n2

2

=n1n2

1

(IC)2= 90A  (IC)2 = 3(IC)1  

(IC)3= 60A  (IC)3 = 2(IC)1  

€

n1n2

3

= 30⇒ n1n2

3

= 2 ⋅ n1n2

1

(V13)1 

(V1)2 = (V13)3  

30o 

λ 

λ 

(J1)1 

(IC)1 = 30A 

€

n1n2

1

=15

30  60  90  120  150  180  210  240  270  300  330  360 

(VL)1 

(Is1)1 

(V13)1  (V23)1  (V21)1  (V31)1  (V32)1 (V12)1 

(J1)1 = (Ip1)1 

(IC)1 

‐(IC)1 

€

n2n1

1

⋅ IC( )1 = x

€

−n2n1

1

⋅ IC( )1 = −x

(V32)1 

30  60  90  120  150  180  210  240  270  300  330  360 

(VL)2 

(Is1)2 

(V2)2  (V3)2 (V1)2 

(J1)2 = (Ip1)2 

(IC)2 

€

23

⋅

n2n1

2

⋅ IC( )2 =23

⋅

n2n1

1

⋅ 3 ⋅ IC( )1[ ] = 2 ⋅ n2

n1

1

⋅ IC( )1

= 2x

€

−13

⋅

n2n1

2

⋅ IC( )2 = −13

⋅

n2n1

1

⋅ 3 ⋅ IC( )1[ ] = −

n2n1

1

⋅ IC( )1 = −xλ 

λ 

(J1)2 

€

n1n2

2

=15

(IC)2 = 90A 

30  60  90  120  150  180  210  240  270  300  330  360 

(VL)3 

(Is1)3 

(V13)3  (V23)3  (V21)3  (V31)3  (V32)3 (V12)3 

(IC)3 

‐(IC)3 

€

n2n1

3

⋅ IC( )3 =12⋅n2n1

1

⋅ 2 ⋅ IC( )1[ ] =

n2n1

1

⋅ IC( )1 = x

€

−n2n1

3

⋅ IC( )3 = −xΔ 

λ 

(J1)3 

€

n1n2

3

= 30

(IC)3 = 60A 

(Ip1)3 

30  60  90  120  150  180  210  240  270  300  330  360 

(VL)3 

(Is3)3 

(V13)3  (V23)3  (V21)3  (V31)3  (V32)3 (V12)3 

(IC)3 

‐(IC)3 

€

n2n1

3

⋅ IC( )3 = x

€

−n2n1

3

⋅ IC( )3 = −xΔ 

λ 

(J1)3 

€

n1n2

3

= 30

(IC)3 = 60A 

(Ip3)3 

€

x

€

−x

Δ 

λ 

(J1)3 

€

n1n2

3

= 30

(IC)3 = 60A 

(Ip3)3 

€

x

€

−x

(Ip1)3 

(J1)3 = (Ip1)3 ‐ (Ip3)3 

€

x€

2x

€

−x

€

−2x

30  60  90  120  150  180  210  240  270  300  330  360 

(J1)3  

€

x€

2x

€

−x

€

−2x30  60  90  120  150  180  210  240  270  300  330  360 

(J1)2  

€

2x

€

−x

(J1)1  

€

x

€

−x

€

J1( )1 =12π

⋅ 2 ⋅ 2π3⋅ x 2

= x ⋅ 2

3

J1( )1 = x ⋅ 23

=n2n1

1

⋅ IC( )1

⋅

23

=115

⋅ 30

⋅23

=1.63A

€

J1( )2 =12π

⋅ 1⋅ 2π3⋅ 2x( )2 +1⋅ 4π

3⋅ x( )2

= x ⋅ 1

2⋅23⋅ 4 +

43

= x ⋅ 1

2⋅123

J1( )2 = x ⋅ 2 =n2n1

1

⋅ IC( )1

⋅ 2 =

115

⋅ 30

⋅ 2 = 2.83A

€

J1( )3 =12π

⋅ 2 ⋅ π3⋅ 2x( )2 + 4 ⋅ π

3⋅ x( )2

= x ⋅ 1

2⋅ 2 ⋅ 1

3⋅ 4 + 4 ⋅ 1

3

= x ⋅ 1

2⋅123

J1( )3 = x ⋅ 2 =n2n1

1

⋅ IC( )1

⋅ 2 =

115

⋅ 30

⋅ 2 = 2.83A

(J1)3  

€

x€

2x

€

−x

€

−2x30  60  90  120  150  180  210  240  270  300  330  360 

(J1)2  

€

2x

€

−x

(J1)1  

€

x

€

−x

ISARE  

30  60  90  120  150  180  210  240  270  300  330  360 

€

−2x

€

−3x

€

5x

€

−4x

€

4x

€

ISARE =12π

⋅ 4 ⋅ π6⋅ 4x( )2 + 2 ⋅ π

6⋅ 5x( )2 + 2 ⋅ π

6⋅ 2x( )2 + 2 ⋅ π

6⋅ 3x( )2

= x ⋅ 12π

⋅ 4 ⋅ π6⋅16 + 2 ⋅ π

6⋅ 25 + 2 ⋅ π

6⋅ 4 + 2 ⋅ π

6⋅ 9

= x ⋅ 12⋅646

+506

+86

+186

= x ⋅ 1

2⋅1406

= x ⋅ 70

6

ISARE = x ⋅ 353

=n2n1

1

⋅ IC( )1

⋅

353

=115

⋅ 30

⋅353

= 6.83A