presentation oh m 1
TRANSCRIPT
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Current FlowConventional Current assumes that current flows out of the positive side of the battery, through the circuit, and back to the negative side of the battery. This was the convention established when electricity was first discovered, but it is incorrect!
Electron Flow is what actually happens. The electrons flow out of the negative side of the battery, through the circuit, and back to the positive side of the battery.
ElectronFlow
Conventional Current
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Engineering vs. ScienceThe direction that the current flows does not affect what the current is doing; thus, it doesn’t make any difference which convention is used as long as you are consistent.
Both Conventional Current and Electron Flow are used. In general, the science disciplines use Electron Flow, whereas the engineering disciplines use Conventional Current.Since this is an engineering course, we will use Conventional Current .
ElectronFlow
Conventional Current
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Ohm’s Law
Quantities Abbreviations Units SymbolsVoltage V Volts VCurrent I Amperes A
Resistance R Ohms Ω
If you know 2 of the 3 quantities, you can solve for the third.
V=IR I=V/R R=V/I
The mathematical relationship between current, voltage, and resistance
Current in a resistor varies in direct proportion to the voltage applied to it and is inversely proportional to the resistor’s value
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Ohm’s Law Chart
VI Rx
Cover the quantity that is unknown.
Solve for V
V=IR
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VI R I=V/R
Ohm’s Law ChartCover the quantity that is unknown.
Solve for I
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VI R R=V/I
Ohm’s Law ChartCover the quantity that is unknown.
Solve for R
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Example: Ohm’s LawThe flashlight shown uses a 6 volt battery and has a bulb with a resistance of 150 . When the flashlight is on, how much current will be drawn from the battery?
VT =+
-VR
IR
Schematic Diagram
mA 40 A 0.04 150V 6
RV I R
R
V
I R
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Circuit Configuration
Series Circuits• Components are
connected end-to-end.• There is only a single
path for current to flow.
Parallel Circuits• Both ends of the components
are connected together.• There are multiple paths for
current to flow.
Components (i.e., resistors, batteries, capacitors, etc.)
Components in a circuit can be connected in one of two ways.
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Series CircuitsA circuit that contains only one path for current flow
If the path is open anywhere in the circuit, current stops flowing to all components.
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Characteristics of a series circuit• The current flowing through every series component is equal.• The total resistance (RT) is equal to the sum of all of the
resistances (i.e., R1 + R2 + R3).
• The sum of all of the voltage drops (VR1 + VR2 + VR3) is equal to the total applied voltage (VT). This is called Kirchhoff’s Voltage Law.
VT
+
-
VR2
+
-
VR1
+ -
VR3
+-RT
IT
Series Circuits
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Example: Series CircuitFor the series circuit shown, use the laws of circuit theory to calculate the following:
• The total resistance (RT)
• The current flowing through each component (IT, IR1, IR2, & IR3)
• The voltage across each component (VT, VR1, VR2, & VR3)• Use the results to verify Kirchhoff’s Voltage Law.
VT
+
-
VR2
+
-
VR1+ -
VR3
+-RT
IT
IR1
IR3
IR2
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Solution:
V
I R
TR R1 R2 R3 Total Resistance:
TT
T
VI (Ohm's Law)R
Current Through Each Component:
Example: Series Circuit
TR 220 470 1.2 k
TR 1900 1.9 k
T
12 vI 6.3 mAmp1.89 k
T R1 R2 R3
Since this is a series circuit:I I I I 6.3 mAmp
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R1 R1V I R1 (Ohm's Law)
Voltage Across Each Component:
V
I R
Example: Series CircuitSolution:
R1V 6.349 mA 220 Ω 1.397 volts
R2 R2V I R2 (Ohm's Law)
R2V 6.349 mA 470 Ω 2.984 volts
R3 R3V I R3 (Ohm's Law)
R3V 6.349 mA 1.2 K Ω 7.619 volts
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T R1 R2 R3V V V V
Verify Kirchhoff’s Voltage Law:
Example: Series CircuitSolution:
1.397 2.984 7.619 12 v v v v
12 v 12 v
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Parallel CircuitsA circuit that contains more than one path for current flow
If a component is removed, then it is possible for the current to take another path to reach other components.
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Characteristics of a Parallel Circuit• The voltage across every parallel component is equal.• The total resistance (RT) is equal to the reciprocal of the sum of the
reciprocal:
• The sum of all of the currents in each branch (IR1 + IR2 + IR3) is equal to the total current (IT). This is called Kirchhoff’s Current Law.321
T
321T
R1
R1
R1
1 R R1
R1
R1
R1
+
-
+
-VR1
+
-VR2 VR3
RT
VT
IT
+
-
Parallel Circuits
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For the parallel circuit shown, use the laws of circuit theory to calculate the following:
• The total resistance (RT)
• The voltage across each component (VT, VR1, VR2, & VR3)
• The current flowing through each component (IT, IR1, IR2, & IR3)
• Use the results to verify Kirchhoff’s Current Law.
19
+
-
+
-
VR1
+
-
VR2 VR3
RT
VT
IT
+
-
IR1 IR2 IR3
Example Parallel Circuits
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Total Resistance:
volts 15V V V V:circuit parallel a is this Since
R3R2R1T
11 1 1T
1 2 3
R
R R R
Voltage Across Each Component:
Solution:Example Parallel Circuits
11 1 1TR
470 2.2 k 3.3 k
346.59 TR = 350
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R1R1
VI (Ohm's Law) R1
V
I R
Current Through Each Component:Solution:
Example Parallel Circuits
R1R1
V 15 vI 31.915 mA=32 mAR1 470
R2R2
V 15 vI 6.818 mA = 6.8 mAR2 2.2 k
.545
R3R3
V 15 vI 4 mA= 4.5mA R3 3.3 k
TT
T
V 15 vI 43.278 mA = 43 mA R 346.59
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Verify Kirchhoff’s Current Law:
T R1 R2 R3I I II
Solution:Example Parallel Circuits
43.278 mA=31.915 mA+6.818 mA+4.545 mA
43.278 mA (43 mA) 43.278 mA (43mA)
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Kirchoff’s Voltage Law
•The algebraic sum of voltage around a loop is zero.
•Assumption:–Voltage drop across each passive element is in the direction of current flow.
1 2 3 4 0V V V V
+ V2 -
- V4 +
+ V3 1+
V
1
-
-
I
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Kirchoff’s Current Law
•Algebraic sum of all currents entering and leaving a node is zero.
•At node A:
•Current entering a node is assigned positive sign. Current leaving a node is assigned a negative sign.
I1
I2
I3A
1 2 3 0I I I
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Law of Voltage division
+ VR1 -
R1
+ VR
2 -
R2
-
V
s
+
I
1
1
1 2R s
RV VR R
2
2
1 2R s
RV VR R
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Law of Current division
R1 R2
-
V
s
+
I
IR2IR1
2
1
1 2R
RI IR R
1
2
1 2R
RI IR R