Resistor (電阻) : R
unit: Ohm (Ω)
( )
V (voltage) = I (current) × R (resistance)
Kirchhoff’s Voltage and Current Laws
1
Ohm’s Law:
V
I=
R
IIt was named
d after
f the
h G
German physicist
h i i Georg
G
Ohm,
Oh who,
h
in a treatise published in 1827, described measurements
of applied voltage and current passing through simple
electrical circuits containing various lengths of wire.
presented a slightly
g y more complex
p
equation
q
than the
He p
one above to explain his experimental results (the above
equation is the modern form of Ohm's law; it could not exist
until
til th
the ohm
h itself
it lf was d
defined
fi d (1861
(1861, 1864))
1864)).
Well before Georg Ohm's work, Henry Cavendish found
experimentally (January 1781) that current varies in direct
proportion to applied voltage, but he did not communicate
his results to other scientists at the time.
From: www.wikipedia.org
2
3
黑
棕
紅
橙
黃
綠
藍
紫
灰
白
4
5
顏色
條紋一
條紋二
條紋三
誤差
黑
0
0
0
10 Ω
= 1Ω
棕
1
1
1
10 Ω
= 10Ω
± 1%
紅
2
2
2
10 Ω
= 100Ω
± 2%
橙
3
3
3
10 Ω
= 1KΩ
黃
4
4
4
10 Ω
= 10KΩ
綠
5
5
5
10 Ω
= 100KΩ
± 0.5%
藍
6
6
6
10 Ω
= 1MΩ
± 0.25%
紫
7
7
7
10 Ω
= 10MΩ
± 0.10%
灰
8
8
白
9
9
± 0.05%
金
-1
10 Ω
= 0.1Ω
± 5%
銀
-2
10 Ω
=0
0.01Ω
01Ω
± 10%
6
4 7 x
102
=
4
4.7
7k
1 0 x 103
= 10 k
3 3 x 102
= 3.3
33k
1 2 x 102
= 1.2 k
5 1 x 100
=
51
7
8
Variable resistors (可變電阻)
9
10
Kirchhoff’s
Kirchhoff
s Voltage Law: conservation of electro
electro-static
static field
ΣV =0
The sum of voltage for a closed loop is zero:
I
R1
I
Vin
R2
•
R3
I
11
I
+
R1
_
+
Vin
R2
V (voltage)
類似攀岩，
垂直上升，或下降。
R3
I (current)
類似水流
類似水流，
從高處向低處流。
_
+
_
I
•
Voltage Law
類似爬山，
從左側出發，
再從右側回來，
高度沒有改變
高度沒有改變。
12
I
0 = Vin – I R1 – I R2 – I R3
+
R1
_
Vin = I R1 + I R2 + I R3
+
Vin = I ( R1 + R2 + R3 )
Vin
R2
_
Vin = I Requivalent
+
R3
_
I
•
Req = R1 + R2 + R3
I=
Vin
( R1 + R2 + R3 )
13
I
+
R1
V1 = I R1 = Vin
R1
R1 + R2 + R3
V2 = I R2 = Vin
R2
R1 + R2 + R3
V3 = I R3 = Vin
R3
R1 + R2 + R3
_
+
Vin
R2
_
+
R3
_
I
•
14
Variable resistors (可變電阻)
n
I
+
n o p
R1
_
Vin
o
+
R2
V2 = I R2 = Vin
_
p
R2
R1 + R2
p
15
Kirchhoff’s
Kirchhoff
s Current Law: conservation of charge
The sum of all currents at a junction is zero:
ΣI=0
IA
0 = + IA – IB – IC – ID
•
IA = IB + IC + ID
ID
IB
IC
16
IA
IA = 2 A,
IB = 6 A
IC = -1 A,
ID = ?
•
ID
IB
IA = IB + IC + ID
ID = 2 – 6 – (-1) = -3 A
IC
17
IA
2A
•
6A
IB
IA = 2 A,
IB = 6 A
IC = -1 A,
ID = -3 A
3A
ID
1A
IC
18
Vin
R1
R2
19
I
•
I1
+
Vin
I2
+
R2
R1
_
_
•
20
I
o
•
n Vin = I1 R1
p
I1
n
+
Vin
I2
+
•
Vin = I2 R2
p
I = I1 + I2
∴
Vin = I Requivalent
R2
R1
_
o
_
1
Req
=
1
R1
+
1
R2
21
V1
V2
R1
V3
R2
R3
22
•
I1
I3
I2
V1
V2
+
V3
+
R1
+
R2
_
R3
_
•
_
•
23
p
•
o
n
I1
I3
I2
V1
V2
+
V3
+
R1
+
R2
_
R3
_
•
_
•
24
p
•
I1
n
V1
I2
o
R2
•
n
0 = I1 R1 + V1 – V2 - I2 R2
o
0 = I2 R2 + V2 – V3 – I3 R3
p
0 = - I1 - I2 - I3
V3
V2
R1
I3
R3
•
25
p
•
I1
n
V1
I2
o
R2
•
n
0 = I1 R1 + V1 – V2 - I2 R2
o
0 = I2 R2 + V2 – V3 – I3 R3
p
0 = - I1 - I2 - I3
V3
V2
R1
I3
R3
•
n
I1 R1 - I2 R2
I2 R2 - I3 R3 = V3 - V2
o
p
= V2 – V1
I1
+ I2
+ I3
= 0
26