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การตอความตานทาน
ความตานทาน (Resistor) เปนคณสมบตของวตถในการขดขวางหรอตานการไหลของกระแสไฟฟาไมใหเคลอนทผานไดสะดวก
RReessiissttoorr CCiirrccuuiittss
การตอความตานทานสามารถตอได 3 แบบ คอ 1. การตอความตานทานแบบอนกรม 2. การตอความตานทานแบบขนาน 3. การตอความตานทานแบบผสม
2
150 Ω 470 Ω 30 Ω
150 Ω
30 Ω
470 Ω
150 Ω
470 Ω
30 Ω
RT = 650 Ω
การตอความตานทานแบบอนกรม
Series Circuits
100 mA 650 Ω 500 Ω 30 Ω
100 mA
100 mA 100 mA
AB
B B
A A
3
การตอความตานทานแบบอนกรม
การตอความตานทานแบบอนกรม หมายถง การนาเอาตวตานทานหรออปกรณไฟฟาตออนดบกน โดยใชปลายของตวทหนงตอกบตนของตวทสอง ปลายของตวทสองตอกบตนของตวทสามเรยงไปตามลาดบ
การตอความตานทานแบบอนกรม กระแสไฟฟาจะไหลในทศทางเดยว (1 Part) และทาใหความตานทานมากขน
ความตานทานรวม RT = R1 + R2 + … + Rn
Series Circuits
4
4 Ω 8 Ω 6 ΩA B
R1 = ? Ω 8 Ω 4 ΩA B
ตวอยางท 1 จากรปจงคานวณหาคาความตานทานรวม (RT)
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ตวอยางท 2 จากรปจงคานวณหาคาความตานทาน R1 เมอ RT = 20 Ω
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5
150 Ω 470 Ω 30 Ω
150 Ω
30 Ω
470 Ω
150 Ω
470 Ω
30 Ω
150 Ω
การตอความตานทานแบบขนาน
Parallel Circuits
15.82 mA 23.73 Ω 28.2 Ω 30 Ω
100 mA
5.05 mA 79.13 mA
A
B
A A
B B
ตทต
เทน
P การต
การานทาน
ทกตวมาอรวมก
การทากน แลนอยกวาห
ความต
Parตอควา
รตอควาหรออปตอรวมนอกท ตอแบบละความหรอเทา
ตานทาน
rallมตาน
ามตานทปกรณไฟกนทจด ทจด ๆบขนาน มตานทาากบคาค
นรวม
lel นทานแ
ทานแบฟฟาตอเด ๆ หนๆ หนง แรงดนานรวมขความตาน
TR
1=
Cirแบบขน
บบขนานเชอมกนนง และ นไฟฟาตของวงจนทานต
1R1
=
rcuนาน
น หน โดยใะปลายข
ตกครอมจรจะตอตวทนอย
2R1
+
uitsมายถง ใชปลายของตวต
มตวตานองมคาตยทสดท
2+ ..
การยของตวตานทาน
นทานทกตอบเทากตออย
R1
+..
รนาเอาตวตานทานทกตวม
กตวจะกบคาท
nR1
6
ตวานมา
7
4 Ω
A
B
6 Ω 8 Ω
ตวอยางท 3 จากรปจงคานวณหาคาความตานทานรวม (RT) ทจด A – B
วธทา
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R 1 R 2 R 3
8
470 Ω 30 Ω
470 Ω 30 Ω
470 Ω 30 Ω
470 Ω 30 Ω
การตอความตานทานแบบผสม
Compound Circuits
500 Ω 100 mA 50 mA
15 Ω 50 mA 50 mA
100 mA
AB
250 Ω
100 mA
AB
235 Ω
9
1. การตอความตานทานแบบอนกรม – ขนาน เปนการนาความตานทานในแตละกลมมาตอกนแบบอนกรมกอน แลวจงนากลมความตานทานแตละกลมมาตอกนแบบขนานกนอกทหนง 2. การตอความตานทานแบบขนาน – อนกรม เปนการนาความตานทานในแตละกลมมาตอกนแบบขนานกอน แลวจงนากลมความตานทานแตละกลมมาตอกนแบบอนกรมกนอกทหนง
การตอความตานทานแบบผสมเราสามารถวเคราะห เพอแกปญหาโจทยไดดงน
พยายามมองรปวงจรวาสวนใดเปนวงจรอนกรมหรอสวนใดเปนวงจรขนาน
ใหยบการตอวงจรทงายและหาคาตอบได โดยจะยบวงจรการตออนกรมกอนการตอขนาน หรอขนานกอนอนกรมกได
รวมคาแลวหาคาความตานทานรวม RT
10
A B
ตวอยางท 4 จากรปจงคานวณหาคาความตานทานรวม (RT) ทจด A – B
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R 1 = 2 Ω R 4 = 4 Ω
R 2 = 2 Ω R 5 = 4 Ω
R 3 = 5 Ω
11
A
B
ตวอยางท 5 จากรปจงคานวณหาคาความตานทานรวม (RT) ทจด A – B
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R 4 = 6 Ω
R 1 =
4 Ω
R 2 =
6 Ω
R 3 = 4 Ω
R 5 =
4 Ω
R 6 =
6 Ω
12
40 Ω 20 Ω
40 Ω 20 Ω
50 Ω
A B
AB
R 1 = 40 Ω R 4 = 20 Ω
R 2 = 40 Ω R 5 = 20 Ω
R 3 = 50 Ω
R 1 = 40 Ω
R 4 = 20 Ω R 5 = 20 Ω
R 2 = 40 Ω
R 3 = 50 Ω
13
A
B
Delta
Delta
วธการเปลยนความตานทานทตอแบบเดลตาใหเปนสตาร
R 4 R 5
R 2 R 1
R 3
R 2
R 3 RY1
RY2 RY3
R 1
14
B
A
การคานวณหาคาความตานทานรวมในวงจร ในกรณทมการตอความตานทานเปนวงจรทสลบซบซอน โยงใยเปนโครงขาย ทาใหการคานวณหาคาความตานทานรวม ไมสามารถคานวณโดยวธการแบบอนกรมหรอขนานได การเปลยนความตานทานทตอแบบเดลตาเปนแบบสตาร จงชวยลดความยงยากในวงจรได
R 5
RY3 RY2
RY1
R 4
15
RY1 = 321
21
RRRRR++
× = ∑ ∆×R
RR 21
RY2 =
321
32
RRRRR++
× = ∑ ∆×R
RR 32
RY3 =
321
13
RRRRR++
× = ∑ ∆×R
RR 13
∑R∆ คอ ผลรวมของความตานทานทงสามตวทตอแบบเดลตา
RY1 , RY2 , RY3 คอ คาความตานทานทตอกนในแบบสตาร
R 3
R 2 RY1
RY3 RY2
R 1
16
A B
A B
Delta
Delta
A B
ตวอยางท 6 จากรป จงคานวณหาคาความตานทานรวม (RT) ทจด A – B
R 4 = 4 Ω
R 5 = 5 Ω
R 3 = 6 Ω
R 1 = 1 Ω
R 3 = 3 Ω
R 2 = 2 Ω
R 4 = 4 Ω
R 5 = 5 Ω
R 3 = 6 Ω
R 1 = 1 Ω
R 3 = 3 Ω
R 2 2 Ω
R 4 = 4 Ω
R 5 = 5 Ω
R 3 = 6 Ω
R 1 = 1 Ω
R 3 = 3 Ω
R 2 = 2 Ω R Y1
R Y2
R Y3
17
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18
A
B
Star
A
B
Star
วธการเปลยนความตานทานทตอแบบสตารใหเปนเดลตา
R 4
R 1
R 3
R 3
R 2
R 4
R 1
R 3
R 5
R 2
19
A
A
Y - ∆ RC
RB R 5
R 2 RA
B
Y - ∆ RC
RB R 5
R 2 RA
B
20
R∆A = 1
133221
RRRRRRR ××× ++ =
1YRR∑ ∆
R∆B =
2
133221
RRRRRRR ××× ++ =
2YRR∑ ∆
R∆C =
3
133221
RRRRRRR ××× ++ =
3YRR∑ ∆
∑R∆ คอ ผลรวมของผลคณของความตานทานแตละคทตอ แบบสตาร ∑R∆ = R1xR2 + R2xR3 + R3xR1
R∆A , R∆B , R∆C คอ คาความตานทานทตอกนในแบบเดลตา
R∆C
R1
R2 R3
R∆B
R∆A
21
A B
ตวอยางท 7 จากรป จงคานวณหาคาความตานทานรวม (RT) ทจด A – B ..........................................................................................................................................................
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R 4 = 4 Ω
R 5 = 5 Ω
R 6 = 6 Ω
R 1 = 1 Ω
R 3 = 3 Ω
R 2 = 2 Ω
22
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25
R1 R2 R3
30 Ω 60 Ω
R2 R1
R4 R3
ใบงานท 1 เรอง การตอเซลลไฟฟา Electric Cell
คาสง จงตอบคาถาม จากโจทยตอไปน 1.1 จากรป ความตานทานจานวน 5 ตวตออนกรมกน จงคานวณหาคาความตานทานรวม
.....................................................................................................……................................................................................................ 1.2 จากรป ความตานทานรวมมคาเทาใด
..........................................................................................................................................………....................................................... 1.5 จากรป ความตานทานจานวน 3 ตวตอขนานกน จงคานวณหาคาความตานทานรวม
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1.6 จากรป จงคานวณหาคาความตานทานรวม
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1.7 จากรป จงคานวณหาคาความตานทานรวม
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R1 R2 R3 R4 R5
2 Ω 2 kΩ 200 Ω 20 kΩ 20 Ω
26
R3 6 Ω R1 4 Ω
R4 10 Ω
R2 R1
R4 R3
R2 5 Ω
R5 5 Ω
200 Ω
200 Ω
1 kΩ 500 Ω
200 Ω 400 Ω
100 Ω
200 Ω
500 Ω
400 Ω
1.8 จากรป จงคานวณหาคาความตานทานรวม
.................................................................................................................................…........................................................................
................................................................................................................................................................................................……..... 1.9 จากรป จงคานวณหาคาความตานทานรวม
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............................................................................................................................................................................................................. 1.10 จากรป จงคานวณหาคาความตานทานรวม
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........................................................................................................................................................................................................…. 1.11 จากรป จงคานวณหาคาความตานทานรวม
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27
200 Ω
500 Ω
600 Ω
100 Ω
300 Ω 100 Ω 1.12 จากรป จงคานวณหาคาความตานทานรวม
..............................................................................................................................................................................................…...........
........................................................................................................................................................................................................…. 1.13 จากวงจรตอไปนจงคานวณหาคา
ก. ความตานทานรวมทจด A – B ข. ความตานทานรวมทจด A – C
ค. ความตานทานรวมทจด A – D ง. ความตานทานรวมทจด B – C
จ. ความตานทานรวมทจด B – D ฉ. ความตานทานรวมทจด C – D
กาหนดให ความตานทาน R1 – R6 มคาความตานทานตวละ 2 Ω ............................................................................................................................................................................................................................
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R1 R2
R5
R3 R4
A
B
C
D R6
28
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29
ใบงานท 2 เรอง การตอเซลลไฟฟา Electric Cell
คาสง จงตอบคาถาม จากโจทยตอไปน
1. จากวงจรตอไปน จงคานวณหาคาความตานทาน RA , RB และ RC โดยใชวธการแปลงจากสตารเปนเดลตาและจากเดลตาเปนสตาร
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............................................................................................................................................................................................................................ 2. จากวงจร จงคานวณหาคาความตานทาน R1 , R2 และ R3 โดยใชวธการแปลงจากสตารเปนเดลตาและจากเดลตา
เปนสตาร
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RB
A
B
R1 1 kΩ C
RA RC
R3 1 kΩ
R2 1 kΩ
A
B
R1 C
R3
R2
RA 6 Ω
RB 4 Ω RC 2 Ω
30
3. จากวงจร จงคานวณหาความตานทานรวมระหวางจด A – B โดยใชวธการแปลงจากสตารเปนเดลตาและจากเดลตาเปนสตาร โดยกาหนดความตานทาน R1 = 2 Ω , R2 = 3 Ω , R3 = 4 Ω , R4 = 2 Ω และ R5 = 3 Ω ............................................................................................................................................................................................................................
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R1 2 Ω
A
B
R2 3 Ω R3 4 Ω
R4 2 Ω R5 3 Ω
31
120 Ω
10 Ω
45 Ω
60 Ω
75 Ω
50 Ω
แบบฝกหด เรอง การตอความตานทานแบบตาง ๆ
คาสง จงตอบคาถามตอไปน
1. ลกษณะการตอแบบอนกรมเปนการตอในลกษณะอยางไร และมคณสมบตอยางไรบาง .............................................................................................................................................................................................................
............................................................................................................................................................................................................. 2. ลกษณะการตอแบบขนานเปนการตอในลกษณะอยางไร และมคณสมบตอยางไรบาง
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............................................................................................................................................................................................................... 3. ผลของการตอความตานทานแบบอนกรม สงผลตอความตานทานในวงจรอยางไร
............................................................................................................................................................................................................... 4. ผลของการตอความตานทานแบบอนกรม สงผลตอความตานทานในวงจรอยางไร
............................................................................................................................................................................................................... 5. กระแสทไหลผานความตานทานทตอแบบอนกรม จะเปนอยางไร
...................................................................................................................................................................................................................... 6. กระแสทไหลผานความตานทานทตอแบบขนาน จะเปนอยางไร
...................................................................................................................................................................................................................... 7. จากรป จงคานวณหาคาความตานทานรวม
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32
20 kΩ
20 kΩ
500 Ω
400 Ω
300 Ω
7. จากรป จงคานวณหาคาความตานทานรวม
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............................................................................................................................................................................................................. 2. จากวงจร จงคานวณหาความตานทานรวมระหวางจด A – B โดยใชวธการแปลงจากสตารเปนเดลตาและจาก
เดลตาเปนสตาร
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R1 2 Ω
A
B
R2 3 Ω R3 4 Ω
R4 4 Ω R6 3 Ω R5 2 Ω
33
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