Circuitos de corriente alterna

1. E2C1A5
Electricity

2. Circuit Analysis with Multisim

3. Circuit Analysis with Multisim
𝑋 𝐿 = 𝜔𝐿 = 2𝜋𝑓𝐿 = 2𝜋 60𝐻𝑧 390𝑚𝐻 = 147.07 Ω
𝑋 𝐶 =
1
𝜔𝐶
=
1
2𝜋𝑓𝐶
=
1
2𝜋(60𝐻𝑧)(47𝜇𝐹)
= 56.44 Ω
𝑍1 = −𝑗𝑋 𝐶 = −𝑗56.44 Ω
𝑍2 = 𝑗𝑋 𝐿 = 𝑗147.07 Ω
𝑍3 = 𝑅1 = 100 Ω
𝑍4 = 𝑅2 = 100 Ω

4. Circuit Analysis with Multisim
𝑍1 = −𝑗𝑋 𝐶 = −𝑗56.44 Ω
𝑍2 = 𝑗𝑋 𝐿 = 𝑗147.07 Ω
𝑍3 = 𝑅1 = 100 Ω
𝑍4 = 𝑅2 = 100 Ω
𝑍 𝑎 = 𝑍2 + 𝑍3 = 𝑗147.07Ω + 100Ω = 100 + j147.07 Ω
𝑍 𝑎 = 100 + j147.07 Ω
𝑍 𝑎 = 177.85∠55.79°
Ω

5. Circuit Analysis with Multisim
𝑍 𝑎 = 100 + j147.07 Ω
𝑍 𝑎 = 177.85∠55.79°
Ω
1
𝑍 𝑏
=
1
𝑍 𝑎
+
1
𝑍4
=
𝑍4 + 𝑍 𝑎
𝑍 𝑎 𝑍4
⇒ 𝑍 𝑏 =
𝑍 𝑎 𝑍4
𝑍4 + 𝑍 𝑎
𝑍 𝑏 =
177.85∠55.79°
Ω 100∠0°
Ω
100 + j147.07 Ω + 100 Ω
= 67.55 + 23.87 Ω
𝑍 𝑏 = 67.55 + j23.87 Ω
𝑍 𝑏 = 71.64∠19.46°
Ω
𝑍1 = −𝑗𝑋 𝐶 = −𝑗56.44 Ω
𝑍2 = 𝑗𝑋 𝐿 = 𝑗147.07 Ω
𝑍3 = 𝑅1 = 100 Ω
𝑍4 = 𝑅2 = 100 Ω

6. Circuit Analysis with Multisim
𝑍 𝑏 = 67.55 + j23.87 Ω
𝑍 𝑏 = 71.64∠19.46° Ω
𝑍1 = −𝑗𝑋 𝐶 = −𝑗56.44 Ω
𝑍2 = 𝑗𝑋 𝐿 = 𝑗147.07 Ω
𝑍3 = 𝑅1 = 100 Ω
𝑍4 = 𝑅2 = 100 Ω
𝑍𝑡 = 𝑍1 + 𝑍 𝑏 == −𝑗56.44 Ω + 67.55 + 23.87 Ω = 67.55 − 𝑗32.57 Ω
𝑍𝑡 = 67.55 − j32.57 Ω
𝑍𝑡 = 74.99∠ −25.74°
Ω

7. Circuit Analysis with Multisim
𝑉𝑠 = 𝐼𝑡 𝑍𝑡 ⇒ 𝐼𝑡 =
𝑉𝑠
𝑍𝑡
=
115∠0° V
74.99∠ −25.74° Ω
= 1.53∠25.74°
A
𝐼 𝑎 =
𝑍 𝑏
𝑍 𝑎
𝐼𝑡 =
71.64∠19.46° Ω
177.85∠55.79° Ω
1.53∠25.74°
A = 0.62∠ −10.59°
A
𝐼4 =
𝑍 𝑏
𝑍4
𝐼𝑡 =
71.64∠19.46° Ω
100∠0° Ω
1.53∠25.74°
A = 1.09∠45.2°
A

8. Circuit Analysis with Multisim
Rectangular form Polar form
Source voltage 115 V 115∠0°
V
Total impedance 67.55 − 𝑗32.57 Ω 74.99∠ −25.74°
Ω
Total current 1.3 + 𝑗0.66 A 1.53∠25.74°
A
Current through L and R1 0.61 − 𝑗0.11 A 0.62∠ −10.59°
A
Current through R2 0.77 + 𝑗0.77 A 1.09∠45.2°
A

9. Circuit Analysis with Multisim
Rectangular form Polar form
Source voltage 115 V 115∠0°
V
Total impedance 67.55 − 𝑗32.57 Ω 74.99∠ −25.74°
Ω
Total current 1.3 + 𝑗0.66 A 1.53∠25.74°
A
Current through L and R1 0.61 − 𝑗0.11 A 0.62∠ −10.59°
A
Current through R2 0.77 + 𝑗0.77 A 1.09∠45.2°
A
𝑍1 = −𝑗𝑋 𝐶 = −𝑗56.44 Ω ⇒ 𝑍1 = 56.44∠ −90° Ω
𝑍2 = 𝑗𝑋 𝐿 = 𝑗147.07 Ω ⇒ 𝑍2 = 147.07∠90°
Ω
𝑍3 = 𝑅1 = 100 Ω ⇒ 𝑍3 = 100∠0° Ω
𝑍4 = 𝑅2 = 100 Ω ⇒ 𝑍4 = 100∠0°
Ω
𝑉1 = 𝐼𝑡 𝑍1 = 1.53∠25.74°
A 56.44∠ −90°
Ω = 86.4∠ −64.26°
V
𝑉2 = 𝐼 𝑎 𝑍2 = 0.62∠ −10.59° A 147.07∠90° Ω = 91.18∠79.41° V
𝑉3 = 𝐼 𝑎 𝑍3 = 0.62∠ −10.59°
A 100∠0°
Ω = 62∠ −10.59°
V
𝑉4 = 𝐼4 𝑍4 = 1.09∠45.2°
A 100∠0°
Ω = 109∠45.2°
V

10. Circuit Analysis with Multisim
Rectangular form Polar form
Source voltage 115 V 115∠0°
V
Total impedance 67.55 − 𝑗32.57 Ω 74.99∠ −25.74°
Ω
Total current 1.3 + 𝑗0.66 A 1.53∠25.74°
A
Current through L and R1 0.61 − 𝑗0.11 A 0.62∠ −10.59°
A
Current through R2 0.77 + 𝑗0.77 A 1.09∠45.2°
A
Capacitor voltage 37.52 − 77.83 V 86.4∠ −64.26°
V
Inductor voltage 16.76 + 𝑗89.63 V 91.18∠79.41°
V
Resistor voltage 1 60.94 − 11.39 V 62∠ −10.59°
V
Resistor voltage 2 76.81 + 𝑗77.34 𝑉 109∠45.2°
V

11. Circuit Analysis with Multisim

12. Circuit Analysis with Multisim
Rectangular form Polar form Vpp Vpp
(Multisim)
Source voltage 115 V 115∠0° V 230 V 229 V
Total impedance 67.55 − 𝑗32.57 Ω 74.99∠ −25.74° Ω
Total current 1.3 + 𝑗0.66 A 1.53∠25.74° A 3.06 A 3.06 A
Current through L and R1 0.61 − 𝑗0.11 A 0.62∠ −10.59° A 1.24 A 1.23 A
Current through R2 0.77 + 𝑗0.77 A 1.09∠45.2° A 2.18 A 2.19 A
Capacitor voltage 37.52 − 77.83 V 86.4∠ −64.26°
V 172.8 V 171 V
Inductor voltage 16.76 + 𝑗89.63 V 91.18∠79.41° V 183.36 V 183 V
Resistor voltage 1 60.94 − 11.39 V 62∠ −10.59° V 124 V 123 V
Resistor voltage 2 76.81 + 𝑗77.34 𝑉 109∠45.2° V 218 V 219 V