Ω p = vi = i r - pa.uky.edukwng/fall2009/phy402/lecture/aug 26.pdfresistance units: [voltage v ......
TRANSCRIPT
![Page 1: Ω P = VI = I R - pa.uky.edukwng/fall2009/phy402/lecture/Aug 26.pdfresistance Units: [Voltage V ... An ideal voltage source should have zero output impedance ⇒δV out =0. Voltmeter](https://reader031.vdocuments.pub/reader031/viewer/2022022011/5b0b630f7f8b9a45518dec76/html5/thumbnails/1.jpg)
Ohm’s Law
V
I
Slope = conductance
=1
resistance
Units:
[Voltage V] = Volt (V)
[Current I] = Ampere (A)
[Resistance R] = Ohm (Ω)
[Power P] = Watt (W)
Ohm’s Law applies only to metal as a conductor.
V = IR
P = VI = I2R
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Example
+ -
Note current direction
100Ω
10V
I
10= 100 I ⇒ I = 0.1A
Power dissipated by the resistor = I2R = (0.1)2(100) = 1W
Power delivered by the battery = VI = (10)(0.1) = 1W
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Color code of resistors
Resistor:
Variable Resistor:
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Example
Value of this resistor = 2600000 Ω ± 5%
![Page 5: Ω P = VI = I R - pa.uky.edukwng/fall2009/phy402/lecture/Aug 26.pdfresistance Units: [Voltage V ... An ideal voltage source should have zero output impedance ⇒δV out =0. Voltmeter](https://reader031.vdocuments.pub/reader031/viewer/2022022011/5b0b630f7f8b9a45518dec76/html5/thumbnails/5.jpg)
Potentiometer (voltage divider)VH
R1
R2
V = VH ⋅R2
R1+R2
(Only if there is no current in
the green line).
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Example10V
99Ω
V = 10 ⋅ = 0.1V1
99+1
1Ω
I = 10/(99+1) = 0.1A
![Page 7: Ω P = VI = I R - pa.uky.edukwng/fall2009/phy402/lecture/Aug 26.pdfresistance Units: [Voltage V ... An ideal voltage source should have zero output impedance ⇒δV out =0. Voltmeter](https://reader031.vdocuments.pub/reader031/viewer/2022022011/5b0b630f7f8b9a45518dec76/html5/thumbnails/7.jpg)
ResistanceThe resistance of a resistor is a constant independent of V. It is also independent of the signal frequency.
V
IFor ALL frequency
Not all devices or components behave like this!
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Example
I
V
Resistance at this point = dV
dI
Diode:
Resistance = dV/dI, depends on the applied voltage.
Capacitor:
Impedance of a capacitor does not depend on the applied voltage, but it depends on the frequency:
Xc = iωC1
![Page 9: Ω P = VI = I R - pa.uky.edukwng/fall2009/phy402/lecture/Aug 26.pdfresistance Units: [Voltage V ... An ideal voltage source should have zero output impedance ⇒δV out =0. Voltmeter](https://reader031.vdocuments.pub/reader031/viewer/2022022011/5b0b630f7f8b9a45518dec76/html5/thumbnails/9.jpg)
Kirchhoff’s Law
ΣI = 0
1. Kirchhoff’s current law: (conservation of charge)
2. Kirchhoff’s voltage law: (conservation of energy)
ΣV = 0
![Page 10: Ω P = VI = I R - pa.uky.edukwng/fall2009/phy402/lecture/Aug 26.pdfresistance Units: [Voltage V ... An ideal voltage source should have zero output impedance ⇒δV out =0. Voltmeter](https://reader031.vdocuments.pub/reader031/viewer/2022022011/5b0b630f7f8b9a45518dec76/html5/thumbnails/10.jpg)
Example 1 (Important)
1
2
1
RV I' (1)
,I' gEliminatin-(2)--- )RI'-(IV-(1)--- RI'V
=⇒
==
R1V R2
II’ I-I’
21
2121
21
21
21
21
21
2
21
RRRR//RR
I RR
RR V
IR VR
RR
IR VRR1
)RRV-(IV
:(2) into Substitute
+=∴
+=⇒
=⎟⎟⎠
⎞⎜⎜⎝
⎛ +⇒
=⎟⎟⎠
⎞⎜⎜⎝
⎛+⇒
=
![Page 11: Ω P = VI = I R - pa.uky.edukwng/fall2009/phy402/lecture/Aug 26.pdfresistance Units: [Voltage V ... An ideal voltage source should have zero output impedance ⇒δV out =0. Voltmeter](https://reader031.vdocuments.pub/reader031/viewer/2022022011/5b0b630f7f8b9a45518dec76/html5/thumbnails/11.jpg)
Example 2 (problem 33 of text)
(3)--- 0 I4I32I- 0)III(2000)II(10001000I
(2)--- 0 II2I- 0)I1000(I1000I1000I
(1)--- 0.012 I23I3I 12 000I23000I3000I
)III(2000)I1000(I 12
321
321323
321
2132
321
321
32121
=++⇒=−−−++
=−+⇒=−−−
=−−⇒=−−⇒
−−+−=
V
1000Ω
12V
1000Ω
1000Ω
1000Ω
2000Ω
I1I2I1- I2
I3 I1- I2- I3I2+ I3
I1
10.154mA 1II
5.583mA I6 I
mA923.0 I 0.012 13I 0.012 I2)3(6I)3(11I
(1) into theseeSubstiutut11I II12I II2I I6 I
I3 I21 I2I
23 II2
I2I23
2 I4I3
I (3)
II2I (2)
31
32
3
3333
3321321
32
323232
3232
1
321
==
==
=⇒=⇒=−−∴
=−=⇒−==⇒
=⇒+=−∴
+=+
=⇒
−=⇒
![Page 12: Ω P = VI = I R - pa.uky.edukwng/fall2009/phy402/lecture/Aug 26.pdfresistance Units: [Voltage V ... An ideal voltage source should have zero output impedance ⇒δV out =0. Voltmeter](https://reader031.vdocuments.pub/reader031/viewer/2022022011/5b0b630f7f8b9a45518dec76/html5/thumbnails/12.jpg)
Input impedence and output impedance
Vin Vout
Iin Iout
Input impedance = ∂Vin∂Iin
Output impedance = - ∂Vout∂Iout
![Page 13: Ω P = VI = I R - pa.uky.edukwng/fall2009/phy402/lecture/Aug 26.pdfresistance Units: [Voltage V ... An ideal voltage source should have zero output impedance ⇒δV out =0. Voltmeter](https://reader031.vdocuments.pub/reader031/viewer/2022022011/5b0b630f7f8b9a45518dec76/html5/thumbnails/13.jpg)
Example
10Ω
9V
8V
Iout
Vout
δVout = 8V-9V = -1V
δIout = 8/10 = 0.8A
Output impedance Xout = -δVout / δIout = -(-1)/0.8 = 1.25Ω
The output impedance of a battery is also known as its internal resistance.
An ideal voltage source should have zero output impedance ⇒ δVout =0
![Page 14: Ω P = VI = I R - pa.uky.edukwng/fall2009/phy402/lecture/Aug 26.pdfresistance Units: [Voltage V ... An ideal voltage source should have zero output impedance ⇒δV out =0. Voltmeter](https://reader031.vdocuments.pub/reader031/viewer/2022022011/5b0b630f7f8b9a45518dec76/html5/thumbnails/14.jpg)
VoltmeterAn ideal voltmeter should have infinite input impedance ⇒ δIin =0
An ideal voltmeter A not so ideal voltmeter
V
Xin
V
How you use a voltmeter:
Voltage difference across these two points=?
V
I IYou want to draw as little current as possible.
Easy!
![Page 15: Ω P = VI = I R - pa.uky.edukwng/fall2009/phy402/lecture/Aug 26.pdfresistance Units: [Voltage V ... An ideal voltage source should have zero output impedance ⇒δV out =0. Voltmeter](https://reader031.vdocuments.pub/reader031/viewer/2022022011/5b0b630f7f8b9a45518dec76/html5/thumbnails/15.jpg)
ExampleA voltmeter with an input impedance of 100kΩ is used to measure the voltage across the Ω resistor of a potentiometer. What will be its reading?
10V
90kΩ
10kΩ V
100kΩ 1V 1090
1010V
:terpotentiome theofoutput al theoretic with the thisCompare
V 0.917 9.09190
9.09110
resistors two theseacross Voltage voltmeter theof Reading
9.091k 1001010010 //100kk10
theory =+
×=
=+
×=
=∴
Ω=+×
=ΩΩ
![Page 16: Ω P = VI = I R - pa.uky.edukwng/fall2009/phy402/lecture/Aug 26.pdfresistance Units: [Voltage V ... An ideal voltage source should have zero output impedance ⇒δV out =0. Voltmeter](https://reader031.vdocuments.pub/reader031/viewer/2022022011/5b0b630f7f8b9a45518dec76/html5/thumbnails/16.jpg)
AmmeterAn ideal ammeter should have zero input impedance ⇒ δVin =0
An ideal ammeter
A
How you use an ammeter:
Current along this line =?
I
Voltage drop across the ammeter should be made as small as possible!
Xin
A
A not so ideal ammeter
A
I
Difficult!
If you do not want to break the circuit, use a current clamp!
![Page 17: Ω P = VI = I R - pa.uky.edukwng/fall2009/phy402/lecture/Aug 26.pdfresistance Units: [Voltage V ... An ideal voltage source should have zero output impedance ⇒δV out =0. Voltmeter](https://reader031.vdocuments.pub/reader031/viewer/2022022011/5b0b630f7f8b9a45518dec76/html5/thumbnails/17.jpg)
AmmeterIf you do not want to break the circuit, use a current clamp!
An ideal ammeter
A
How you use an ammeter:
Current along this line =?
I
Voltage drop across the ammeter should be made as small as possible!
Xin
A
A not so ideal ammeter
A
I
Difficult!
![Page 18: Ω P = VI = I R - pa.uky.edukwng/fall2009/phy402/lecture/Aug 26.pdfresistance Units: [Voltage V ... An ideal voltage source should have zero output impedance ⇒δV out =0. Voltmeter](https://reader031.vdocuments.pub/reader031/viewer/2022022011/5b0b630f7f8b9a45518dec76/html5/thumbnails/18.jpg)
Example
0.0901A 100091.9
resistor 100 rough theCurrent th ammeter theof Reading
V091.910100
10010
resistor100 theacross Voltage
==
Ω=∴=
+×=
Ω
An ammeter is constructed by connecting a 100Ω in parallel to an ideal voltmeter and used to measure the current in a simple circuit. What will be its reading?
10Ω
10VI=?
10Ω
10VI=? V100Ω
Ammeter
1A 1010 I
:insertedammeter thout thecurrent wi of valueal theoretic with the thisCompare
theory ==
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Current and voltage sourcesAn ideal voltage source should have zero output impedance ⇒ δVout =0
An ideal voltage source
V
V
Xout
A not so ideal voltage source
An ideal current source should have infinite output impedance ⇒ δIout =0
An ideal current source
Xout
A not so ideal current source
e+ -
Textbook symbol:
My symbol:
II
How to measure V and Xout?
How to measure I and Xout?
![Page 20: Ω P = VI = I R - pa.uky.edukwng/fall2009/phy402/lecture/Aug 26.pdfresistance Units: [Voltage V ... An ideal voltage source should have zero output impedance ⇒δV out =0. Voltmeter](https://reader031.vdocuments.pub/reader031/viewer/2022022011/5b0b630f7f8b9a45518dec76/html5/thumbnails/20.jpg)
ExampleWe can construct a current source from a voltage source
106Ω 9V
Current source106Ω 9V
10Ω
I=9/(100+106)
=8.99991×10-7A106Ω 9V
1000Ω
I=9/(1000+106)
=8.9910×10-7A
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Thevenin (voltage source)TheoremConsider a circuit made of batteries and resistors only. Any two points on the circuit can be considered as the terminals of a not so ideal voltage source.
Complicated circuit made of batteries and resistors only.
AB
=V
Xout
A B
With respect to points A and B, the whole circuit can be represented by two parameters – the electromotive force V and the internal resistance Xout of the not so ideal voltage source.
Note that if you choose another two points, the parameters V and Xoutwill change their values also!
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Norton (current source)TheoremConsider a circuit made of batteries and resistors only. Any two points on the circuit can be considered as the terminals of a not so ideal current source.
Complicated circuit made of batteries and resistors only.
AB
=A B
With respect to points A and B, the whole circuit can be represented by two parameters – the current I and the internal resistance Xout of the not so ideal current source.
Note that if you choose another two points, the parameters I and Xoutwill change their values also!
Xout
I
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ExampleWe can construct a current source from a voltage source
106Ω 9V
Current source
106Ω 9V
10-6A
1V
Xout = 106Ω
V
Xout
=
Xout
I=VXout