engineering fundamentals session 4 (3 hours). resistance amount of current flows in an electric...
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Engineering Engineering FundamentalsFundamentalsEngineering Engineering
FundamentalsFundamentals
Session 4 (3 hours)Session 4 (3 hours)
Resistance
• Amount of current flows in an electric circuit depends on the resistance of the material through which it travels
I=V/R• A resistor is a device which provides resistance
in an electrical circuit
R=V/I
• SI unit is ohm, written as 1 =1 VA-1
• An electric circuit is a connection of sources and loads in any way which allow charge to flow.e.g. a simple circuit with a battery and
a light bulb
• Relationship between current direction and voltage polarity
V=____
V=_____
I
+ 10V -
• Consider the following circuit:
– What is the voltage VR through the 5 resistor, and its polarities?
– What is the current I, and its direction?
+
V
-
10+V-
5
VR
5
Measuring resistance
• Voltmeter-ammeter method
R=V/I
• Multimeter• What is the resistance of your body?
A
V
• An open circuit occurs when a conductor is broken between the points under test.
• A short circuit occurs when a low resistance conductor such as a wire is connected
R=____
R=____
Ohm’s Law • Voltage across two ends of a
resistor is directly proportional to the current flowing through it.
I
V
V-I graph for a resistor that obeys Ohm’s law
V=IRI
+ V -
Resistors in series
• A series circuit has only one path for current to flow– Example:
– Same current through each resistor I = I1 = I2
R2R1
+ V1- + V2 -
I
+ V -
I1 I2
– Applying Ohm’s law to each resistor,V1 = IR1, V2 = IR2
– Voltage of the source equals sum of V1 and V2
V = V1 + V2
= IR1 + IR2
= I (R1 + R2) = I R
– Equivalent resistance R = R1 + R2
– In general
R = R1 + R2 + R3 + • • • + Rn
R1 R2 R3
• • •Rn
• Example:
– What is the equivalent resistance?– What are the currents I1, I2 through the
resistors?– What are their directions?– What is the voltage across each
resistor?
Indicate the relative voltage polarities (+,-)
12V
2 4
V1 V2
I
I1 I2
• Solution:
– Equivalent resistance = 2 + 4 = 6– Current I = V/R = 12V/6 =2A
12V
2 4
12V
6
+ 12V -
2 4
I
I1 I2
• Solution:– V = IR
Voltage across 2 resistor = 2A*2 = 4V
Voltage across 4 resistor = 2A*4 = 8V
+ 12V -
2 4
+ 4V - + 8V -
I
I1 I2
• Consider the following circuit:
– What are the voltages V1, V2, V3, and V4, and their corresponding polarities 極性 ?
– What is the current? and its direction?
+
V
-
10
V1
5
V3
V2
V4
5
5 5
• Consider the following circuit:
– What are the voltages V1, V2, V3, and V4, and their corresponding polarities?
– What is the current, and its direction?
+
V
-
10
V1
5
V3
V2
V4
5
5 5
Resistors in Parallel
• A parallel circuit has more than one path for current to flow– Example:
– Same voltage across each resistorV = V1 = V2
R2
R1
+ V2 -
+ V1 -
I2
I1
+ V -I
– Applying Ohm’s law to each resistor,V = I1R1, V = I2R2
– Sum of current in branches equal to current I I = I1 + I2 = V/R1+V/R2
= V (1/R1+1/R2) = V 1/R
– Equivalent resistance 1/R = 1/R1+1/R2
– In general
1/R = 1/R1+1/R2+1/R3+ • • •+1/Rn
R1
R2
R3
Rn
...
• Consider the following with R1 > R2
What can be said about the equivalent resistance R ?
(a) R > R1
(b) R2 < R < R1
(c) R < R2
R1
R2
R
• Example:
– What is the equivalent resistance?– What are the currents through the resistors and
their directions?– What is the total current?
12V
2
4
• Solution:
– Equivalent resistance:1/R = 1/R1+1/R2 = 1/2 + 1/4 = 3/4
R = 4/3– Same voltage across each resistor = 12V
I1 =current through 2 =V/R1 =12V/2=6A
I2 =current through 4=V/R2=12V/4=3A
– Total current I = I1 + I2 = 6A + 3A = 9A
12V
2
4
12V
4/3
I
I1
I2
• Example:
– What is the equivalent resistance?
– What is the supply voltage (Vs)?
– What are the voltages across AB (VAB), BC (VBC)?
What are the currents through the resistors (I20, I30) ?
30unknown
voltage supply
10
20
B
C
A
2A+
V s
-
+ V AB -
+
V BC
-I20 I30
• Solution:
– Equivalent resistance
R = 22
30unknown
voltage supply
10
20
B
C
A
2A
unknown
voltage supply
10
12
B
C
A
2A
unknown
voltage supply
22
B
C
A
2A
• Solution:
– Supply voltage
Vs =IR=2A*22=44V– Voltage across AB,
VAB=2A*10 =20V
Voltage across BC, Vbc=V-VAB=44V-20V=24V
30unknown
voltage supply
10
20
B
C
A
2A
unknown
voltage supply
10
12
B
C
A
2A+
V s
-
+
V s
-
+ V AB - + V AB -
+
V BC
-
+
V BC
-
• Solution:
– Current through 20 resistor
I1 = VBC/ 20 = 1.2A
– Current through 30 resistor
I2 = VBC/ 30 = 0.8A
Check total current
I1 + I2 = 1.2A + 0.8A = 2A
30unknown
voltage supply
10
20
B
C
A
2A I1 I2
• Some problems to work in class:– Problem 1:
• What is the equivalent resistancebetween A and B?
3
9
9
B
A
9
3
3
– Problem 2:
• What is the equivalent resistance between A and B?
8
8
BA
8
8