Tarea 1 Seminario

𝐸𝑆

𝑍𝐿𝐷
𝑍𝐿𝑁

𝐼̃ =
𝐼̃

𝐸̃𝑆

𝐸̃𝑆
𝑍̃𝐿𝑁 + 𝑍̃𝐿𝐷

𝑍̃𝐿𝑁 = 𝑍𝐿𝑁 ∠𝜃

𝐼=

𝑍̃𝐿𝐷 = 𝑍𝐿𝐷 ∠𝜙

𝐸𝑆
√(𝑍𝐿𝑁 cos 𝜃 + 𝑍𝐿𝐷 cos 𝜙)2 + (𝑍𝐿𝑁 sin 𝜃 + 𝑍𝐿𝐷 sin 𝜙)2

𝐼=

1 𝐸𝑆
√𝐹 𝑍𝐿𝑁

𝑍𝐿𝐷 2
𝑍𝐿𝐷
𝐹 =1+(
) + 2(
) cos(𝜃 − 𝜙)
𝑍𝐿𝑁𝑍𝐿𝑁

𝑉𝑅 = 𝑍𝐿𝐷 𝐼 =

𝑃𝑅 = 𝑉𝑅 𝐼 cos 𝜙 =

1 𝑍𝐿𝐷
𝐸𝑆
√𝐹 𝑍𝐿𝑁

𝑍𝐿𝐷 𝐸𝑠 2
(
) cos 𝜙
𝐹 𝑍𝐿𝑁

tan 𝜃 = 10

cos 𝜙 = 0.95

𝑍𝐿𝑁
𝑍𝐿𝐷

𝑉𝑅
𝑃𝑅𝑀𝐴𝑋 =

=1

(𝐸𝑆 )2
1
cos 𝜙
1 + (1)2 + 2(1) cos(𝜃 − 𝜙) 𝑍𝐿𝑁

𝑍𝐿𝐷
𝐸 2
∗ (𝑍 𝑠 )cos 𝜙
𝑍
𝑍
𝐿𝑁
1 + ( 𝐿𝐷 ) + 2 ( 𝐿𝐷 ) cos(𝜃 − 𝜙)
𝑍𝐿𝑁
𝑍𝐿𝑁
=
(𝐸𝑆 )2
1
cos 𝜙
2
1 + (1) + 2(1) cos(𝜃 − 𝜙) 𝑍𝐿𝑁
2

𝑃𝑅
𝑃𝑅𝑀𝐴𝑋

𝑍𝐿𝐷
𝑍𝐿𝑁
𝑍 2
𝑍
1 + (𝑍𝐿𝐷 ) + 2 (𝑍𝐿𝐷 ) 0.405226
𝐿𝑁
𝐿𝑁
=
1
1 + (1)2 +2(1)0.405226
𝑍𝐿𝐷
(2 + 2 ∗ 0.405226)
𝑍𝐿𝑁
=
𝑍 2
𝑍
1 + (𝑍𝐿𝐷 ) + 2 (𝑍𝐿𝐷 ) 0.405226
𝐿𝑁
𝐿𝑁
𝑍𝐿𝑁
(2 + 2 ∗ 0.405226)
𝑍𝐿𝐷
=
𝑍 2
𝑍
1 + ( 𝐿𝑁 ) + 2 ( 𝐿𝑁 ) 0.405226
𝑍𝐿𝐷
𝑍𝐿𝐷

𝑉𝑅 = 𝑍𝐿𝐷 𝐼 =
𝑉𝑅
=
𝐸𝑆

=

1 𝑍𝐿𝐷
𝐸𝑆
√𝐹 𝑍𝐿𝑁

12
√1 + (𝑍𝐿𝐷 ) + 2 (𝑍𝐿𝐷 ) cos(𝜃 − 𝜙)
𝑍𝐿𝑁
𝑍𝐿𝑁

𝑍𝐿𝐷
𝑍𝐿𝑁

1
2
√1 + (𝑍𝐿𝑁 ) + 2 (𝑍𝐿𝑁 ) cos(𝜃 − 𝜙)
𝑍𝐿𝐷
𝑍𝐿𝐷

𝐼𝑆𝐶 =

𝐼
𝐼𝑆𝐶

𝐸𝑆
𝑍𝐿𝑁

1 𝐸𝑆
𝑍𝐿𝑁
= √𝐹
𝐸𝑆
𝑍𝐿𝑁
=

1
√𝐹
1

=

2
√1 + (𝑍𝐿𝐷 ) + 2 (𝑍𝐿𝐷 ) cos(𝜃 − 𝜙)𝑍
𝑍
𝐿𝑁

=

𝐿𝑁

1
2
√1 + (𝑍𝐿𝑁 ) + 2 (𝑍𝐿𝑁 ) cos(𝜃 − 𝜙)
𝑍𝐿𝐷
𝑍𝐿𝐷

𝑍𝐿𝑁
𝑍𝐿𝐷

𝑃𝑅𝑀𝐴𝑋 =

𝑃𝑅
𝑃𝑅𝑀𝐴𝑋

(𝐸𝑆 )2
1
1 + (1)2 + 2(1) cos(𝜃) 𝑍𝐿𝑁

𝑍𝐿𝐷
𝐸𝑠 2
∗
(
𝑍𝐿𝑁 ) cos 𝜙
𝑍𝐿𝐷 2
𝑍𝐿𝐷
1+(
) + 2(
) cos(𝜃 − 𝜙)
𝑍𝐿𝑁
𝑍𝐿𝑁=
(𝐸𝑆 )2
1
2
1 + (1) + 2(1) cos(𝜃) 𝑍𝐿𝑁
𝑍𝐿𝐷
∗ cos 𝜙
𝑍
𝑍
1 + (𝑍𝐿𝐷 ) + 2 (𝑍𝐿𝐷 ) cos(𝜃 − 𝜙)
𝐿𝑁
𝐿𝑁
=
1
1 + (1)2 + 2(1) cos(𝜃)
2

𝑍𝐿𝐷
(2 + 2 cos(𝜃))
𝑍𝐿𝑁
=
cos 𝜙
𝑍𝐿𝐷 2
𝑍𝐿𝐷
1 + (𝑍 ) + 2 (𝑍 ) cos(𝜃 − 𝜙)𝐿𝑁
𝐿𝑁
𝑍𝐿𝑁
(2 + 2 cos(𝜃))
𝑍𝐿𝐷
=
cos 𝜙
𝑍 2
𝑍
1 + ( 𝐿𝑁 ) + 2 ( 𝐿𝑁 ) cos(𝜃 − 𝜙)
𝑍𝐿𝐷
𝑍𝐿𝐷

𝑃𝑅
𝑃𝑅𝑀𝐴𝑋

𝑉𝑅
𝐸𝑆

𝑄𝑅 = √𝑆𝑅 2 − 𝑃𝑅2

Codigo de matlab
a)
clear
x=0:0.01:3;
for i=1:1:301y(i)=(x(i)*(2+2*0.405226)/(1+x(i)^2+2*x(i)*0.405226));
end
plot(x,y)
hold on
x=0:0.01:3;
for i=1:1:301
z(i)=1/(1+x(i)^2+2*x(i)*0.405226)^(1/2);
end
plot(x,z)
x=0:0.01:3;
for i=1:1:301w(i)=x(i)/(1+x(i)^2+2*x(i)*0.405226)^(1/2);
end
plot(x,w)
hold off

b)
i)
clear
x=0:0.1:300
s1=0.9
s2=0.95
s3=1
for i=1:3001
y1(i)=x(i)*(2+2*cos(atan(10)acos(1)))*s1/(1+x(i)^2+2*x(i)*cos(atan(10)-acos(s1)));...