The document discusses different types of electric cell connections. It describes series, parallel, and combination connections. For a series connection, the voltage adds up but the current remains the same. For a parallel connection, the current adds up but the voltage remains the same. A combination connection uses both series and parallel configurations together. Calculations are provided for voltage, current, and resistance based on the number and properties of the cells in each type of connection.

1. ก ก ก
1 (2104-2102)
2
! "##$ %# ก & ' (
) *+ก,- .
%/ ก ก0 #+ #+ 1 1
0 +ก 12 ก .ก ก *3ก4
ก *3ก4 5ก

2. 2 "##$ %# ก & ' (
6, 1$ +
)! ' (/7( .1 . 7(1 . 8( ' ก ก+ "##$ %# ก & "##$ )! ' (
6, 1$ )9&ก .
1. ก ก )!; < 8 ,(
2. ก1 . . 8 "##$ % <.=7. ,(
3. ก1 . . 8 "##$ % 6& =7. ,(
4. ก 5ก & "##$ )! ' ( ,(
5. 1 % ,+ กก & 8 "##$ ,(

3. 7 2.1 ก )!; < 8
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ก ก )!; < 8 ก ,( ก )!; < 3 1!
1) % # ก0 , ! 1 ! ก0 , "3 W )#+ 8( 7
2) X #, (Load) ! = "3 W )#+ [7ก' ( ! W
)#+ ; #! ก
3) & ! "3 W [ ,)#+ ก% # ก0 , . +
X #,
0 + ' ก ; ก# [3 % # ก0 , ' ก % & "3
' ก]1! % & & ! ก "##$
2.1 "##$ (Electric Cell)
"##$ . [3 6 ก 2$ # )#+ 1. W )#+ X1 ( = ' 8
"##$ ก ,( %/ #]กX , (Electrode) 2 %/ ;0 #]กX #&$%# = !
X1 ( 0 + 6(. "##$ &+ 8 "##$ 1. ,(%ก % & & (Battery) [ b
W &( 0 + +#+ก42$8 "##$ 1. ,+ % , ' 7 2.2
7 2.2 +#+ก42$ "##$

4. ' % & & . 1$ ก 1! "##$ "3 .&+; %& 3 "##$83; ' %&# "##$
.8+; #] ก X , 2 8+; 1! 8+; #] ก X ,# W X# + ก %# 8+; #] ก X , ก W
X# %, .! ## 7' "##$ 0 cก ก+ 8+; #]กX ,# "3 W + ก
cก 1. 0 ' ( %, . #]ก& ).83; ' ก#+ ก+ ## 0 cก ก+
8+; #]กX , ก W %, cก 1. 0 ' ( + ก 7 #]ก& W /#' (8+;
#]กX , ก . #]ก& ก 8+; #]กX ,# . #]ก& '
W /#' ( ก,1 .& *+ก $ 83; 8+; #]กX ,X# +; 8+; ; ./#' ( . [' ( W
% # % ,+ ! % # ก0 , ก % & ,(
7 2.3 "##$ % )!; <
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' "##$ , +; /#8 ก ก, cก ## ก+ 8+; #]กX , .
/#' ( ก,ก 3กก 8 8+; #]กX , , ] , ] %# .! 8+; #]กX ,[7ก 0 # .,
% & & ก] . . [' ( ,( "##$ , ; . ! h "##$ <.=7. (Primary Cell)i
% && , ;. . [ 0 +, 6 (Charge) ' . ,(%# + . ! ก ! "##$ %
% ( (Dry Cell) ) ## ' (8( ' W % % (
+ . "##$ . [ 0 +, 6 ' . (Recharge) ,( ! ก cก = '
"##$ . 0 ' ( ก,ก 3กก 8 8+; #]กX , .! "##$ [7ก' ( ., . [ 0 +,
6' . ก% # ก % = ก ก "##$ 6& =7. (Secondary Cell) %# + . !
กก "##$ % m ก (Wet Cell) ) ## ' (. [ W 8 #

5. 2.2 ก & "##$
! ก "##$ %&# "##$ .% ,+ 1 "##$ W [ b
' .% ,+ 1 1.5 X #&$& "##$ ! & ก( % & & .8 & . ( &# , ' ( ก]
.8 , 6 X #&$ 12 X #&$%# 24 X #&$ W &( %&[( &( ก ' (% ,+ %&ก& ก .
7 &( 0 "##$ . & )! ' ( ,(% ,+ & . &( ก X, ก & "##$ . [%
ก ,(,+ ;
1) ก & "##$ % 6ก .
- ก & "##$ % .% ,+
- ก & "##$ % +ก#( % ,+
2) ก & "##$ % 8
-ก & % 8 .1,1 1 .&( = ' "##$
-ก & % 8 1,1 1 .&( = ' "##$
3) ก & "##$ % / .
- ก & "##$ % 6ก .-8
-ก & "##$ % 8 - 6ก .
2.3 ก & "##$ % 6ก . (Series Cell Connection)
ก & "##$ % 6ก . 1! ก 0 "##$ .& ก+ ! & + ,+ ก+
2.3.1 ก ก
' ก & "##$ % 6ก . .% ,+ ' ก & % ;8+; 8 "##$
. * , ก+ %# & W %[ ก+ X, ก 0 8+; # 8 "##$ 1 & ก+ 8+; ก8
"##$ "##$ 2 %# 8+; ก8 "##$ 3 & ก+ 8+; # 8 "##$ 2 %# & ,+ ; ! p
7 2.4 ก & "##$ % .% ,+ .1,1 .&( = '
,(
E T = E AB = E 1 + E 2 + E 3 + ... + E n (2.1)

6. 7 2.5 ก & "##$ % .% ,+ %# 1,1 1 .&( = '
ก 7 2.5 ,(
E T = E AB = E 1 + E 2 + E 3 + ... + E n
%#
rT = rAB = r1 + r2 + r3 + ... + rn (2.2)
2.1 "##$ 0 3 "##$ %&# "##$.1 % ,+ 1.5 X #&$ ' %&# "##$.1 .
&( = ' 0.1 X $. [( 0 . & 6ก .% .% ,+ .% ,+ .
%# 1 .&( = ' .
E1 E2 E3
ET
7 2.6
7 2.7
!" % ,+ . E T = E1 + E 2 + E 3

7. = 1.5 + 1.5 + 1.5
= 4.5 V
1 .&( = ' . rT = r1 + r2 + r3
= 0.1 + 0.1 + 0.1
= 0.3 Ω
2.3.2 ก ก #ก $
' ก & "##$ % 6ก . +ก#( % ,+ ; 0 ' (% ,+ #,# %&1 .
&( = ' . (rT) .1 ก+ /# .8 1 .&( = ' 8 %&# "##$ .ก+
ET
7 2.7 % , ก & "##$ % 6ก . +ก#( % ,+
7 2.8 % , +#+ก42$ก & "##$ % +ก#( % ,+
ก 7 2.8 ,(
ET = E1 - E 2 (2.3)
ก 2 E1 . กก E2
%#
ET = E 2 - E1 (2.4)
ก 2 E2 . กก E1

8. [( 1,1 .&( = ' "##$ ,(1 1 .&( = ' .
rT = r1 - r2 (2.5)
2.2 "##$ . "##$& 6ก .ก+ ,+ 7 1 % ,+ .%# 1 .&(
= ' .
.! E1 = E2 = E3 = 5 V %# r1 = r2 = r3 = 2 Ω
7 2.9
!" % ,+ ET = E1 + E2 - E3
= 5+5w5
= 5 V
1 .&( = ' . rT = r1 + r2 + r3
= 2+2+2
= 6 Ω
2.4 ก & "##$ % 8 (Parallel Cell Connection)
' ก & "##$ % 8 +; "##$ 0 . ' (& 8 &( .8 ,% ,+
ก+ ก & "##$ % 8 . [3 ก 0 "##$ &+; %& 2 "##$83; . & 8 ก+
! & 1 .ก+ X, & ' #+ก42 8+; .! ก+ & .ก+ W 6, , %# 8+; #! ก] 0 . &
. W 6, , ก+ ,+ % , ' 7 2.10 ก & "##$ % 8 ./#' ( ,(ก %
#' ).. ก83; ) "##$ %&# "##$ & % 8 ก % ก.

9. ET
7 2.10 ก & ##$ % 8
2.4.1 ก & '( ) ) $ ! * +
7 2.11
ก 7 2.11 ,(
E1 = E2 = V (2.6)
E1 E2 V
IT = = = (2.7)
R R R
I
I1 = I2 = T (2.8)
n
.! n 1! 0 "##$ 0.& 8 ก+
IT = I1 + I 2 (2.9)
2.4.2 ก & !() ) $ ! * +
7 2.12

10. ก 7 2.12 ,( "##$ E1 .1 .&( = ' 1! r1 %# "##$ E2 .1 .
&( = ' 1! r2 [( 1 .&( = ' 8 %&# "##$.1 1 .&( ก+ . . [
1 1 .&( = ' "##$ . (rT) ,+ +;
.! r1 = r2
,(
1 1 1
= + (2.10)
rT r1 r2
r ×r
! rT = 1 2 (2.11)
r1 + r2
r r
! rT = 1 = 2 (2.12)
n n
.! n 1! 0 "##$ & 8 ก+
RT = rT + R (2.13)
E1 E2
,( IT = = (2.14)
RT RT
V = I T .R (2.15)
E1 - V
I1 = (2.16)
r1
E -V
I2 = 2 (2.17)
r2
2.3 "##$ .% ,+ 9 V 1 .&( = ' 8 %&# "##$.1 "##$# 2 Ω 0 .
& 8 ก+ ,+ 7
7 2.13
!"
r1 × r2
rT =
r1 + r2
2× 2
=
2+2

11. = 1 Ω
RT = rT + R
= 1 + 12
= 13 Ω
E1 E2
IT = =
RT RT
9
=
13
= 0.69 A
V = I T .R
= 0.69 × 12
= 8.31 V
E1 - V
I1 =
r1
9 - 8.31
=
2
= 0.345 A
E2 - V
I2 =
r2
9 - 8.31
=
2
= 0.345 A
IT
! I1 =
n
0.69
=
2
= 0.345 A
IT
I2 =
n
0.69
=
2
= 0.345 A
2.5 ก & "##$ % / . (Combination Cell Connection)
ก & "##$ % / . 1! ก 0 "##$ . & ' #+ก42 6ก .%# 8 .ก+
' . [& ,( 2 5 1!

12. 2.5.1 ก ก -& 1! ก 0 "##$ # p "##$. & 6ก .
ก+ W ก#6.ก ก +; %#( 0 ก#6. "##$%&# ก#6.. & 8 ก+ ก ,+ 7 2.14
7 2.14
ก 7 2.14 ,(
ET1 = E1 + E2
%# ET2 = E3 + E4
V
IT =
rT + R
.! rT1 = r1 + r2
rT2 = r3 + r4
rT1 × rT2
rT =
rT1 + rT2
I
I1 = T
2
I
I2 = T
2
%# IT = I1 + I2
2.4 ก 7 2.14 1 I1, I2, IT %# V
.! r1 = r2 = r3 = r4 = 1 Ω %# E1 = E2 = 3 V ,E3 = 4 V ,E4 = 2 V
%# R = 5 Ω
!" ET1 = E1 + E2

13. = 3+3
= 6 V
ET2 = E3 + E4
= 4+2
= 6 V
ET = ET1 = ET2 = V = 6 V
rT1 = r1 + r2
= 1+1
= 2 Ω
rT2 = r3 + r4
= 1+1
= 2 Ω
rT1 × rT2
rT =
rT1 + rT2
4× 4
=
4+4
16
=
8
= 2 Ω
ET
IT =
rT + R
6
=
2+5
6
=
7
= 0.857 A
V = IT.R
= 0.857 × 5
= 4.285 V
E T1 - V
I1 =
rT1
6 - 4.285
=
4
1.715
=
4
= 0.429 A

14. E T2 - V
I2 =
rT2
6 - 4.285
=
4
1.715
=
4
= 0.429 A
2.5.2 ก & - ก 1! ก 0 "##$ . & 8 ก+ ก W ก#6.
%#( 3 0 ก#6.8 "##$ & 8 ก+ . & 6ก .ก+ ก ,+ 7 2.15 .! % ,+ %#
1 .&( = ' 8 %&# "##$.1 ก+
IT
I1 I2
r1 E T1 r2
E1 E2
R V
I3 I4
r3 r4
E T2
E3 E4
7 2.15
ก 7 2.15 ,(
E1 = E2
E3 = E4
' ( ET = E1 + E3
! ET = E2 + E4
r1 × r2
rT1 =
r1 + r2
r ×r
rT2 = 3 4
r3 + r4
rT = rT1 + rT2

15. RT = rT + R
ET
IT =
RT
= I1 + I 2
= I3 + I4
IT
I1 = I2 = I3 = I4 =
2
ET1 = E1 w I1.r1 ! E2 w I2.r2
ET2 = E3 w I3.r3 ! E4 w I4.r4
2.5 ก ' 7 2.15 1 IT, I1, I2, I3, I4, ET1, ET2 %# V
.! r1 = r2 = r3 = r4 = 2 Ω %# E1 = E2 = E3 = E4 = 6 V
R= 6 Ω
!" ก E1 = E2 = 6 V
E2 = E2 = 6 V
' ( ET = E1 + E2
= 6+6
= 12 V
r1 × r2
rT1 =
r1 + r2
2× 2
=
2+2
= 1Ω
r3 × r4
rT2 =
r3 + r4
2× 2
=
2+2
= 1Ω
rT = rT1 + rT2
= 1+1
= 2Ω
RT = rT + R
= 2+6
= 8Ω

16. ET
IT =
RT
12
=
8
= 1.5 A
IT
I1 = I2 = I3 = I4 =
2
1.5
=
2
= 0.75 A
ET1 = E1 w I1.r1
= 6 w (0.75 × 2)
= 4.5 V
ET2 = E3 w I3.r3
= 6 w (0.75 × 2)
= 4.5 V
V = IT.RT
= 1.5 × 8
= 12 V