ΠΠ½Π°Π»ΠΈΠ· ΡΠ΅ΠΏΠ΅ΠΉ ΠΏΠΎΡΡΠΎΡΠ½Π½ΠΎΠ³ΠΎ ΡΠΎΠΊΠ°
1/20)β’Ρ1+(11/120)β’Ρ2-(1/60)β’Ρ3=43/6. 40β’i11+130β’i22−20β’i33−70β’i44=-450. R9=(R5β’R3)/(R4+R5+R3)=2400/120=20 ΠΠΌ. R8=(R4β’R5)/(R4+R5+R3)=1200/120=10 ΠΠΌ. R7=(R4β’R5)/(R4+R5+R3)=1200/120=10 ΠΠΌ. I2=(Ρ4-Ρ3+E2)/R2=(-Ρ3+E2)/R2=3.3416 A. 7381β’40β1,1747β’20β0,6005β’60=50. 30,055+1502,505+2377,1168=3849,4768 ΠΡ. 5/56)β’Ρ1-(1/20)β’Ρ2-(1/40)β’Ρ3=0. Pi Π½Π°Π³Ρ=?Pi ΠΈΡΡ=3849,4768 ΠΡ. 50β’0,6011+450β’3,3389+8β’297,1396… Π§ΠΈΡΠ°ΡΡ Π΅ΡΡ >
ΠΠ½Π°Π»ΠΈΠ· ΡΠ΅ΠΏΠ΅ΠΉ ΠΏΠΎΡΡΠΎΡΠ½Π½ΠΎΠ³ΠΎ ΡΠΎΠΊΠ° (ΡΠ΅ΡΠ΅ΡΠ°Ρ, ΠΊΡΡΡΠΎΠ²Π°Ρ, Π΄ΠΈΠΏΠ»ΠΎΠΌ, ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½Π°Ρ)
1. ΠΠ°Π΄Π°Π½ΠΈΠ΅
R1=70 ΠΠΌ. R2=20 ΠΠΌ. R3=40 ΠΠΌ. R4=20 ΠΠΌ. R5=60 ΠΠΌ. R6=40 ΠΠΌ. IK1=8 A. IK2=0 A. IK3=0 A. E1=0 B. E2=450 B. E3=0 B. E4=0 B. E5=-50 B. E6=0 B. | ||
- 2. Π Π°ΡΡΠ΅Ρ ΡΠ΅ΠΏΠΈ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΊΠΎΠ½ΡΡΡΠ½ΡΡ ΡΠΎΠΊΠΎΠ²
- (R3+R4+R5)I11-R3I22-R5I33-R4I44=-E5
- -R3I11+(R1+R2+R3)I22-R2I33-R1I44=-E2
- -R5I11-R2I22+(R5+R2+R6)I33=E2+E5
I44=IK1
ΡΠΎΠΊ ΠΊΠΎΠ½ΡΡΡΠ½ΡΠΉ ΠΌΠΎΡΠ½ΠΎΡΡΡ Π³Π΅Π½Π΅ΡΠ°ΡΠΎΡ
- 120β’I11-40β’I22-60β’I33-20β’I44=50
- -40β’I11+130β’I22-20β’I33-70β’I44=-450
- -60β’I11-20β’I22+120β’I33=400
I44=8.
I11=6.8277 A.
I22=4.0899 A.
I33=7.4288 A.
I44=8 A.
I1=I22-I44=-3.9101 A.
I2=I33-I22=3.3389 A.
I3=I11-I22=2.7378 A.
I4=I11-I44=-1.1723 A.
I5=I33-I11=0.6011 A.
I6=I33=7.4288 A.
- 3. Π Π°ΡΡΠ΅Ρ ΡΠ΅ΠΏΠΈ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΡΠ·Π»ΠΎΠ²ΡΡ ΠΏΠΎΡΠ΅Π½ΡΠΈΠ°Π»ΠΎΠ²
- (1/R1+1/R3+1/R4)β’Ρ1-(1/R3)β’Ρ3-(1/R4)β’Ρ2=0
- (1/R4+1/R5+1/R6)β’Ρ2-(1/R4)β’Ρ1-(1/R5)β’Ρ3=IK1+E5/R5
- (1/R2+1/R3+1/R5)β’Ρ3-(1/R3)β’Ρ1-(1/R5)β’Ρ2=-E5/R5+E2/R2
Ρ4=0.
- (5/56)β’Ρ1-(1/20)β’Ρ2-(1/40)β’Ρ3=0
- (-1/20)β’Ρ1+(11/120)β’Ρ2-(1/60)β’Ρ3=43/6
- (-1/40)β’Ρ1-(1/60)β’Ρ2+(11/120)β’Ρ3=70/3
Ρ1=273.6416 Π.
Ρ2=297.1396 Π.
Ρ3=383.1687 Π.
I1=(Ρ4-Ρ1)/R1=-Ρ1/R1=-3.9092 A.
I2=(Ρ4-Ρ3+E2)/R2=(-Ρ3+E2)/R2=3.3416 A.
I3=(Ρ3-Ρ1)/R3=2.7381 A.
I4=(Ρ1-Ρ2)/R4=-1.1747 A.
I5=(Ρ3-Ρ2+E5)/R5=0.6005 A.
I6=(Ρ2-Ρ4)/R6=Ρ2/R6=7.4285 A.
4. ΠΡΠΎΠ²Π΅ΡΠΊΠ° ΠΏΠΎ Π·Π°ΠΊΠΎΠ½Π°ΠΌ ΠΠΈΡΡ Π³ΠΎΡΠ°
ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΡΠΎΠΊΠΈ.
I1, Π. | I2, Π. | I3, Π. | I4, Π. | I5, Π. | I6, Π. | ||
ΠΠΠ’. | — 3.9101. | 3.3389. | 2.7378. | — 1.1723. | 0.6011. | 7.4288. | |
ΠΠ£Π. | — 3.9092. | 3.3416. | 2.7381. | — 1.1747. | 0.6005. | 7.4285. | |
ΠΡΠΎΠ²Π΅ΡΠΊΠ° ΠΏΠ΅ΡΠ²ΡΠΌ Π·Π°ΠΊΠΎΠ½ΠΎΠΌ ΠΠΈΡΡ Π³ΠΎΡΠ° (ΡΠΎΠΊΠΈ ΠΈΠ· ΠΠΠ’).
I1+I3-I4=0. | — 3.9101+2.7378+1.1723=0. | — Π²ΡΠΏΠΎΠ»Π½ΡΠ΅ΡΡΡ. | |
IK1+I4+I5-I6=0. | 8−1.1723+0.6011−7.4288=0. | — Π²ΡΠΏΠΎΠ»Π½ΡΠ΅ΡΡΡ. | |
— I2+I3+I5=0. | — 3.3389+2.7378+0.6011=0. | — Π²ΡΠΏΠΎΠ»Π½ΡΠ΅ΡΡΡ. | |
— I6+IK1+I1+I2=0. | — 7.4288+8−3.9101+3.3389=0. | — Π²ΡΠΏΠΎΠ»Π½ΡΠ΅ΡΡΡ. | |
ΠΡΠΎΠ²Π΅ΡΠΊΠ° Π²ΡΠΎΡΡΠΌ Π·Π°ΠΊΠΎΠ½ΠΎΠΌ ΠΠΈΡΡ Π³ΠΎΡΠ° (ΡΠΎΠΊΠΈ ΠΈΠ· ΠΠ£Π).
I3R3+I4R4-I5R5=-E5 | 2,7381β’40−1,1747β’20−0,6005β’60=50. | — Π²ΡΠΏΠΎΠ»Π½ΡΠ΅ΡΡΡ. | |
I1R1-I3R3-I2R2=-E2 | — 3,9092β’70−2,7381β’40−3,3416β’20=-450. | — Π²ΡΠΏΠΎΠ»Π½ΡΠ΅ΡΡΡ. | |
I6R6+I2R2+I5R5=E2+E5 | 7,4285β’40+3,3416β’20+0,6005β’60=400. | — Π²ΡΠΏΠΎΠ»Π½ΡΠ΅ΡΡΡ. | |
- 5. ΠΠ°Π»Π°Π½Ρ ΠΌΠΎΡΠ½ΠΎΡΡΠ΅ΠΉ
- ?Pi Π½Π°Π³Ρ=?Pi ΠΈΡΡ=3849,4768 ΠΡ.
- ?Pi Π½Π°Π³Ρ=I12R1+I22R2+I32R3+I42R4+I52R5+I62R6=
=(-3,9101)2β’70+(3,3389)2β’20+(2,7378)2β’40+(-1,1723)2β’20+(-0,6011)2β’60+(7,4288)2β’40=.
=1070,2217+222,9651+299,822+27,4857+21,6793+2207,4828=.
=3849,477 ΠΡ.
?Pi ΠΈΡΡ=E5I5+E2I2+IK1Ρ2=.
=-50β’0,6011+450β’3,3389+8β’297,1396=.
=-30,055+1502,505+2377,1168=3849,4768 ΠΡ.
6. ΠΠ΅ΡΠΎΠ΄ ΡΠΊΠ²ΠΈΠ²Π°Π»Π΅Π½ΡΠ½ΠΎΠ³ΠΎ Π³Π΅Π½Π΅ΡΠ°ΡΠΎΡΠ°
ΠΏΠΎΡΠ΅Π½ΡΠΈΠ°Π»Ρ Ρ2 ΠΈ Ρ3 Π² ΠΎΡΡΡΡΡΡΠ²ΠΈΠΈ Π²Π΅ΡΠ²ΠΈ Ρ ΡΠΎΠΏΡΠΎΡΠΈΠ²Π»Π΅Π½ΠΈΠ΅ΠΌ R1 ΠΠ£Π ΡΠ·Π΅Π» 2: (1/R4+1/R5+1/R6)β’Ρ2-(1/(R3+R4)+1/R5)β’Ρ3=IK1+E5/R5
ΡΠ·Π΅Π» 3: -(1/(R3+R4)+1/R5)β’Ρ2+(1/R2+1/R3+1/R5)β’Ρ3=E2/R2-E5/R5
- (11/120)β’Ρ2-1/30β’Ρ3=43/6
- (-1/30)β’Ρ2+(11/120)β’Ρ3=70/3
Ρ2=196.4673 Π.
Ρ3=325.7965 Π.
ΠΠΠ=UΠ₯Π₯ ΡΠΊΠ²ΠΈΠ²Π°Π»Π΅Π½ΡΠ½ΠΎΠ³ΠΎ Π³Π΅Π½Π΅ΡΠ°ΡΠΎΡΠ°.
UXX=Ρ4-Ρ1=-Ρ1=-(Ρ4-I2R2+E2-I34β’R3)=I2R2+I34R3-E2 Π.
I2=(Ρ4-Ρ3+E2)/R2=(-Ρ3+E2)/R2=(-325.7965+450)/20=6.2102 A.
I34=(Ρ3-Ρ2)/(R3+R4)=(325.7965−196.4673)/(40+20)=2.1555 A.
UXX=6.2101β’20+2.1555β’40−450=124.202+86.22−450=-239.578 Π.
R8=(R4β’R5)/(R4+R5+R3)=1200/120=10 ΠΠΌ.
R9=(R5β’R3)/(R4+R5+R3)=2400/120=20 ΠΠΌ.
R7=(R4β’R5)/(R4+R5+R3)=1200/120=10 ΠΠΌ.
R10=R8+R6=10+40=50 ΠΠΌ.
R11=R9+R2=20+20=40 ΠΠΌ.
RΠΠΠ=(R10β’R11)/(R10+R11)+R7=2000/90=32,2222 ΠΠΌ.
I1=UXX/RΠΠΠ+R1=62,5648 Π.
7. ΠΠΎΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½Π°Ρ Π΄ΠΈΠ°Π³ΡΠ°ΠΌΠΌΠ°
Ρ4=0 Π. Ρ43=Ρ4-I2R2=-I2R2=. =-3.3389β’20=-66.778 Π. Ρ3=383.1687 Π. Ρ32=Ρ3-I5R5=383.1687−0.6011β’60=347.1027 Π. Ρ2=297.1396 Π. | ||