Chapter 2 – Resistive Circuits
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Transcript of Chapter 2 – Resistive Circuits
Fall 2001 ENGR201 Circuits I - Chapter 2 1
Chapter 2 – Resistive Circuits
• Read pages 14 – 50• Homework Problems - TBA
Objectives:• to learn about resistance and Ohm’s Law• to learn how to apply Kirchhoff’s laws to resistive
circuits• to learn how to analyze circuits with series and/or
parallel connections• to learn how to analyze circuits that have wye or
delta connections
Fall 2001 ENGR201 Circuits I - Chapter 2 2
Resistance - Definition
• Resistance is an intrinsic property of matter and is a measure of how much a device impedes the flow of current.
• The greater the resistance of an object, the smaller the amount of current that will flow for a given applied voltage.
• The resistance of an object depends on the material used to construct the object (copper has less resistance than plastic), the geometry of the object (size and shape), and the temperature of the object. (R = L/A)
Fall 2001 ENGR201 Circuits I - Chapter 2 3
Resistance – Applications
• Sometimes we want to minimize the resistance of an object (in a conductor, for instance).
• Sometimes we want to maximize the resistance (in an insulator).
• Sometimes we to relate the resistance of the object to some physical parameter (such as a photoresistor or RTD).
• Sometimes we want to precisely control the resistance of an element in order to influence the behavior of a circuit such as an amplifier.
Fall 2001 ENGR201 Circuits I - Chapter 2 4
Resistance - Sizing
Resistors come in all shapes and sizes (see Figure 2.1 in your text). However, several common parameters are used to characterize resistors:
ohmic value (nominal) measured in Ohms (), maximum power rating measured in Watts
(W), and precision (or tolerance) measured as a
percentage of the ohmic value.
Fall 2001 ENGR201 Circuits I - Chapter 2 5
Ohm’s Law - describes the relationship between the current through and the voltage across a resistor.
Different devices connected to a power source demand different amounts of power from that source. That is, different devices present differing amounts of loading.
The 6w bulb offers more resistance to the flow of current than the 12w bulb.
I = 0.5A I = 1A
12V12V 6W 12W
Ohm’s Law
Fall 2001 ENGR201 Circuits I - Chapter 2 6
• Rather than specify the load that a device represents in terms of its voltage/power rating, we can specify that load in terms of its resistance.
• The smaller the resistance the greater the load (the greater the power demand).
Ohm’s Law – Mathematical Definition
R = V/II = V/R V = IR
+V-
R I
I = 0.5A I = 1A
12V12V 6W 12W
R = 12V/0.5A = 24 R = 12V1A = 12
Fall 2001 ENGR201 Circuits I - Chapter 2 7
How much current will a 12V/12W lamp demand if 6V is applied to it? How much power is demanded?
6V12V 12W 12W
Example
A 12w/12v lamp will draw 1A of current:• P = VI 12W = 12V I I = 1A• V = IR (Ohm’s Law) R = 12V/1A = 12• Therefore, if V = 6V I = 6V/1A = 12 • P = 6v 0.5A = 3W = 0.25 12W. • Since both the voltage and current are halved, the
power is cut by a factor of four.
Fall 2001 ENGR201 Circuits I - Chapter 2 8
R is the resistance of the device, measured in ohms (). The greater the value of R, the smaller the value of I.
R = V/I +V-
I = 0A
12V
Open Circuit, R = I = 0 regardless of the value of V (NO LOAD)
(air, plastic, wood)
Short & Open Circuits
Short Circuit, R =0V = 0 regardless of thevalue of I
(wire)
I =
12V V
Fall 2001 ENGR201 Circuits I - Chapter 2 9
• Ohms’ law relates the magnitude of the voltage with the magnitude of the current AND
• the polarity of the voltage to the direction of the current.
Resistors always absorb power, so resistor current always flows through a voltage drop.
+V-
I = V/RR
Ohm’s Law – Voltage Polarity & Current Direction
Fall 2001 ENGR201 Circuits I - Chapter 2 10
Ohms’ Law can be represented graphically – called a VI characteristic:
+V-
R I = V/R
I
V
m = Slope = V/I = R
Ideal resistor, VI characteristic
Ohm’s Law - Graphically
Fall 2001 ENGR201 Circuits I - Chapter 2 11
V
I
Short circuit, slope = 0 (V = 0)
Open circuit, slope = (I = 0)
V
I
Practical resistor VI characteristic
Pmax
Pmax
Non-ideal Resistors
Fall 2001 ENGR201 Circuits I - Chapter 2 12
• Resistance is a measure of how much a device impedes the flow of current. Conductance is a measure of how little a device impedes the flow of current.
• Resistance and conductance are simply two different ways to describe the voltage-current characteristic of a device.
• At times, especially in electronic circuits, it is advantageous to work in terms of conductance rather than resistance
Conductance
Fall 2001 ENGR201 Circuits I - Chapter 2 13
Resistance: R = V/I, (ohms)
+V-
Conductance:G = I/V, S(seimens)
+V-
(G = 1/R = R-1)
Conductance - Units
Old style symbol for conductanceOld style units = mho
Fall 2001 ENGR201 Circuits I - Chapter 2 14
P = VI (any device)for a resistor:P = V(V/R) = V2/RorP = (IR)I = I2R
P = VI (any device)In terms of conductance:P = V(VG) = V2GorP = (I/G)I = I2/G
Resistance: R
+V-
I
V = IR = I/G
Resistance – Power Equations
P = VIP = V2/RP = I2R
Fall 2001 ENGR201 Circuits I - Chapter 2 15
Kirchhoff’s Laws• Kirchhoff’s Current Law (KCL)• Kirchhoff’s Voltage Law (KVL)
A node is a “point” in a circuit where two or elements are connected.
RR R+
-
Node-A
Kirchhoff’s Laws
RR R
Node-A
+-
Fall 2001 ENGR201 Circuits I - Chapter 2 16
Kirchhoff’s Current Law
• The algebraic sum of all currents at any node in a circuit is exactly zero.
• The sum of all currents entering = sum of all currents leaving
• We neither gain nor lose current at a node.
I1
I2 I3R
R R+-
Node-A
I4
I1-I2+I3-I4 = 0
I1+I3 = I2+I4
KCL
Fall 2001 ENGR201 Circuits I - Chapter 2 17
Kirchhoff’s Voltage Law (KVL)
A loop is a closed path about a circuit that begins and ends at the same node. However, no element may be traversed more than once.
A
B C D
E
Five loops in the circuit shown are:
A-C-B-A
A-D-C-A C-D-E-C
B-C-E-B
A-D-E-B-AAre there more loops ?
KVL
Fall 2001 ENGR201 Circuits I - Chapter 2 18
• The algebraic sum of all voltages about any loop in a circuit is exactly zero.
• The sum of all increases (rises) = sum of all voltage decreases (drops)
• We do not gain or lose voltage if we start and end at the same node.
A
BC D
E
+ V1 -
- V2 +
+ V3
-
+ V4-+
V5 -
+ Vx -+ V6-
+ Vy-
By KVL:• V2 + V3 - V1 = 0• -V3 + V4 - Vx = 0• V1 + Vy - V6 = 0• Vx + V5 -Vy = 0• V2 + V4 + V5 - V6 = 0
KVL
Fall 2001 ENGR201 Circuits I - Chapter 2 19
Two circuits are equivalent if, for any source connected to the circuits, they demand the same amount power. The two circuits “look” the same to the source
I1
+
-Vs
Device
#1
P1 = VSI1
I2
+
-Vs
Device
#2
P2 = VSI2
P1 = P2 VSI1 = VSI2 I1 = I2
If the applied voltage is the same, two equivalent circuits will demand the same amount of current from the source.
EquivalentCircuits
Fall 2001 ENGR201 Circuits I - Chapter 2 20
Rab
a
b
a
b
R1
R4
R3R2
R6 R5
Rab
Series connection (all elements have the same current)
a
b
R1
R4
R3R2
R6 R5
VabI Vab
I
Rab
Vab = I Rab
Series Resistance
Fall 2001 ENGR201 Circuits I - Chapter 2 21
By KCL: IR1 = IR2 = … = IR6 = IBy KVL: Vab = IR1+ IR2+ IR3+ IR4+ IR5+ IR6Vab/I = (R1 + R2 + R3 + R4 + R5 + R6) = Rab
a
b
R1
R4
R3R2
R6 R5
VabI Vab
I
Ra
b
Vab = I Rab
The equivalent resistance of two or more series-connected resistors is the sum of the individual resistors.
Series Resistance
Fall 2001 ENGR201 Circuits I - Chapter 2 22
Parallel connection (all the elements have the same voltage)
Vab/I = Rab
Parallel Resistance
Vab
I
Rab
Vab
I
R1 R2 R3 R4 R5
A
B
by KCL:I = I1 + I2 + I3 + I4 + I5I = Vab/R1 + Vab/R2 + Vab/R3 + Vab/R4 + Vab/R5I = Vab[R1-1 + R2-1 + R3-1 + R4-1 + R5-1 ]Vab/I = [R1-1 + R2-1 + R3-1 + R4-1 + R5-1 ]-1
Fall 2001 ENGR201 Circuits I - Chapter 2 23
Vab
I
Rab
Vab
I
R1 R2 R3 R4 R5
Vab/I = Rab
Rab = [R1-1 + R2-1 + R3-1 + R4-1 + R4-1 ]-1
Since G = 1/R = R-1
Rab = [G1 + G2 + G3 + G4 + G5]-1
Gab = G1 + G2 + G3 + G4 + G5
Parallel Resistance
Fall 2001 ENGR201 Circuits I - Chapter 2 24
The total voltage applied to a group of series-connected resistors will be divided among the resistors. The fraction of the total voltage across any single resistor depends on what fraction that resistor is of the total resistance.
a
b
R1
R4
R3R2
R6 R5
VabI
RTOTAL = Rab = R1 + R2 + R3 + R4 + R5 + R6
+V4
-
4
4
1 2 3 4 5 6ab
RV V
R R R R R R
The Voltage Divider Rule (VDR)
Fall 2001 ENGR201 Circuits I - Chapter 2 25
The total current applied to a group of resistors connected in parallel will be divided among the resistors. The fraction of the total current through any single resistor depends on what fraction that resistor is of the total conductance.
GTOTAL = R1-1 + R2 -1 + R3 -1 + R4 -1 + R5 -1
1
5 1 1 1 1 1
5 5
1 2 3 4 5Total TotalTotal
G RI I I
G R R R R R
I5
VabR1 R2 R3 R4 R5
ITotal
The Current Divider Rule (CDR)
Fall 2001 ENGR201 Circuits I - Chapter 2 26
For two resistors:1
2
1 2Total
RI I
R R
Itotal = I1 + I2
R1 R2I1
I2
2
1
1 2Total
RI I
R R
CDR – Two Resistors
Observations:• The smaller resistor will have the larger current.• If R1= R2, then I1 = I2
• If R1 = nR2, then I2 = nI1