Electro-figura 3.docx

FIGURA 3 MALLAS

𝐼3 = −30,30 𝑚𝐴 ↻= 30,30 𝑚𝐴 ↺ CORRIENTES EN LAS RESISTENCIAS

MALLA 1 −10 + 220 𝐼1 + 330𝐼1 − 330𝐼2 = 0

𝐼220 = 𝐼1 = 20,71 𝑚𝐴

550𝐼1 − 330𝐼2 = 10 ①

𝐼330 = 𝐼1 − 𝐼2 = (20,71 − 4,22)𝑚𝐴

MALLA 2

𝐼330 = 16,49 𝑚𝐴

330𝐼2 − 330𝐼1 + 470𝐼2 + 100𝐼2 − 100𝐼3 = 0

𝐼470 = 𝐼2 = 4,22 𝑚𝐴

−330𝐼1 + 900𝐼2 − 100𝐼3 = 0 ②

𝐼100 = 𝐼3 + 𝐼2 = (30,30 + 4,22)𝑚𝐴

MALLA 3 100𝐼3 − 100𝐼2 + 150𝐼3 + 8 = 0

𝐼100 = 34,52 𝑚𝐴 𝐼150 = 𝐼3 = 30,30 𝑚𝐴 NODOS

−100𝐼2 + 250𝐼3 = −8 ③ DETERMINANTES 550 |A| = −330 0 |𝐴1 | =

−330 0 900 −100 = 91025000 −100 250

10 −330 0 0 900 −100 = 1886000 −8 −100 250

VOLTAJES NODALES 𝑣1 = 10 V 𝑣4 = 8 V 𝐼1 =

𝑣1 −𝑣2 220

𝑣

𝐼5 =

𝑣3 − 𝑣4 150

2 𝐼2 = 330

550 10 0 |A2 | = −330 0 −100 = 385000 0 −8 250

LCK – NODOS V2 Y V3

550 −330 |A3 | = −330 900 0 −100

𝐼3 − 𝐼4 − 𝐼5 = 0 ②

10 0 = −2758800 −8

CORRIENTES EN LAS MALLAS 𝐼1 =

|𝐴1 | 1886000 = = 20,71 𝑚𝐴 |𝐴| 91025000

𝐼2 =

|𝐴2 | 385000 = = 4,22 𝑚𝐴 |𝐴| 91025000

𝐼3 =

|𝐴3 | −2758800 = = −30,30 𝑚𝐴 |𝐴| 91025000

𝐼1 = 20,71 𝑚𝐴 ↻ 𝐼2 = 4,22 𝑚𝐴 ↻

𝐼3 =

𝑣2 −𝑣3 470

𝐼1 − 𝐼2 − 𝐼3 = 0 ①

REEMPLAZANDO EN ① 10 − 𝑣2 𝑣2 (𝑣2 − 𝑣3 ) − − =0 220 330 470 10 𝑣2 𝑣2 𝑣2 𝑣3 − − − + =0 220 220 330 470 470 −301 𝑣2 𝑣3 10 + =− ① 31020 470 220 REEMPLAZANDO EN ② 𝑣2 − 𝑣3 𝑣3 𝑣3 − 𝑣4 − − =0 470 100 150

𝑣

3 𝐼4 = 100

FIGURA 3 𝑣2 𝑣3 𝑣3 𝑣3 8 − − − + =0 470 470 100 150 150 𝑣2 53 𝑣3 8 − =− 470 2820 150

②

DETERMINANTES − |A| =

301 1 31020 470 = 331 1 53 1861200 − 470 2820

|𝐴| = 1,778 ∗ 10−4 10 1 470 = 1501 |𝐴1 | = 220 8 53 1551000 − − 150 2820 −

|𝐴1 | = 9,677 ∗ 10−4 − |𝐴2 | =

301 10 − 31020 220 = 1429 1 8 2326500 − 470 150

|𝐴2 | = 6,142 ∗ 10−4 VOLTAJES NODALES 𝑣1 = 10 V 𝑣4 = 8 V 𝑉1 = 𝑣2 =

|𝐴1 | 9,677 ∗ 10−4 = = 5,41 𝑉 |𝐴| 1,778 ∗ 10−4

𝑉2 = 𝑣3 =

|𝐴2 | 6,142 ∗ 10−4 = = 3,43 𝑉 |𝐴| 1,778 ∗ 10−4

VOLTAJES EN LAS RESISTENCIAS 𝑣220 = 𝑣1 − 𝑣2 = 10𝑉 − 5,41𝑉 = 4,59 𝑉 ↻ 𝑣330 = 𝑣2 = 5,41 𝑉 ↻ 𝑣470 = 𝑣2 − 𝑣3 = 5,41𝑉 − 3,43𝑉 = 1,98𝑉 ↻

𝑣100 = 𝑣3 = 3,43 𝑉 ↻ 𝑣150 = 𝑣3 − 𝑣4 = 3,43𝑉 − 8𝑉 = −4,57𝑉 ↻

𝑣150 = 𝑣4 − 𝑣3 = 8𝑉 − 3,43𝑉 = 4,57 ↺

FIGURA 3