17.5 series and parallel resistors ;kirchhoffs rules statement of kirchhoffs rules junction rule ( i...
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17.5 series and parallel resistors ;Kirchhoff’s rules
Statement of Kirchhoff’s Rules• Junction Rule ( I = 0)– The sum of the currents entering any point must
equal the sum of the currents leaving that junction• A statement of Conservation of Charge
• I1 = I2 + I3
outin II
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– You must go around the loop in one direction– The sum of the measured will equal zero
Loop Rule ( V = 0)The sum of the potential changes around any
closed circuit loop must be zero
(a) The voltage across a battery is taken to be positive (a voltage rise) if traversed from – to + and negative if traversed in the opposite direction.
(b) The voltage across a resistor is taken to be negative (a drop) if the loop is traversed in in the direction of the assigned current and positive if traversed in the opposite direction
Vba = - IR
Vba = IR
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ExampleCalculate the current I flowing into the node
outin II
(3+ I ) A = 2 AI = 2 -3 = -1 A
The current flowing into the node is – 1 A which is the same as +1 A flowing out of the node
ExampleCalculate the current I defined in the diagram
I +2 A = - 4 AI = (- 4 – 2 ) A = - 6 AI is in the opposite directionI + I = 6 AI = ( 6 – 6 ) A = A
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Kirchhoff’s rules :The sum of the potential changes around any closed circuit must be zero
There are “two” ways to connect circuit elements.
1) Series combination: R3R2R1
+ -
ε
I
III
V1 V3V2
( a )
Rs
+ -
V
I
ε ( b )
) 12 . 17 (
0
0
321
321
321
321
RRRR
RRRI
RIRIRIVVV
RIRI
s
ss
Apply the Loop Rule
Figure 17- 10 (a) three resistors in series ( b) the equivalent resistance Rs leads to the same current I,
The current is the same in resistors because any charge that flows through one resistor flows through the other but the potential differences across them are not the same
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2) Parallel combination
(a )
( b )
13 17. 1111
111
111
OR
leaving that equalmust A point entering
321
321
321321
3
3
2
2
1
1
321
RRRR
RRRR
RRRRRRI
RI
RI
RI
RI
IIII
currentthe
p
p
p
I
Figure 17 .11 ( a ) three resistors in parallel . ( b ) the equivalent single resistance Rp produces the same current I
V
Rp
+ -
I
IA B
Iε
R3
R2
R1
+ -
I
I3
I1
I2
A B
Iε
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Example 17.10(a ) find the equivalent resistance of the resistors in figure 17.10 a ( b ) the current I in each resistor
(a )
(b )
( c )
Solved in the text book
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T.Norah Ali Almoneef 8
V20 10
I 30
From the circuit with source voltage V and Total current I, which resistor will have the greatest voltage across it?The resistor with the largest resistance (30 )
Which resistor has the greatest current flow through it?Same for all because series circuit
If we re-ordered the resistors, what if any of this would change?Nothing would change
Conceptoal question
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A) find the current in the circuit shown in the figure .B ) find the potential difference across each circuit element
In the figure, we had a 3kΩ, 10 kΩ, and 5 kΩ resistor in series,
AI 5.0
VV
VV
VV
5.2
5
5.1
3
2
1
Example
18kRs
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ExampleFrom the figure find ( a ) I ( total current ) , Rp ( total resistance ) ( b ) I 1 , I 2 , I 3
AI 23 AI 32
AI 61
AI 11
64.1 R p
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Four resistors are connected as shown in figure. Find the equivalent resistance between points a and c.
A. 4 R.
B. 3 R.
C. 2.5 R.
D. 0.4 R.
E. Cannot determine from information given
.
Example
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V2010
I 30
From the circuit with source voltage V and Total current I, which resistor will have the greatest voltage across it?The resistor with the largest resistance (30 )
Which resistor has the greatest current flow through it?Same for all because series circuit
If we re-ordered the resistors, what if any of this would change?Nothing would change
Conceptual questions
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I
Total resistance would increaseTotal current would decreaseVoltage across each resistor would decrease (All voltage drops must still sum to total in series circuit; Kirchhoff’s law of voltages)Current through each resistor would be lower (total current decreased, but same through each one)
• If we added a resistor in series with these, what would happen to the total resistance, total current, voltage across each resistor, and current through each resistor?
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from the circuit with source voltage V and Total current I, which resistor will have the greatest voltage across it?All the same in parallel branches Which resistor has the greatest current flow through it?The “path of least resistance” (10) What else can you say about the current through each branch?They will sum to the total I (currents sum in parallel circuits; Kirchhoff’s law of current)
Conceptual questions
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• If we added a resistor in parallel with these, what would happen to the total resistance, total current, voltage across each resistor, and current through each resistor?Total resistance would decreaseTotal current would increaseVoltage across each resistor would still be VCurrent through each resistor would be higher and would sum to new total
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17.12 Kirchhoff’s rules in complex circuits Kirchhoff’s rules permit us to analyze any dc circuit .including circuits too complex Using the two rules (1) the sum of all the potential drops around any closed path in a circuit is equal to zero. (2) The current entering any point = The current leaving.
Example 17.15
Find the current in the circuit shown in the figure
Solved in the text book
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A) 2 A
B) 3 A
C) 5 A
D) 6 A
E) 10 A
5 A
8 A
2 A
P
What is the current in branch P?
The current entering the junction in red is 8 A, so the current leaving must also be 8 A. One exiting branch has 2 A, so the other branch (at P) must have 6 A.
5 A
8 A
2 A
P
Junction
6 A
SS
Conceptual questions
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2 V
2
6 V
4 V
3 1
1
I1 I3
I2
Which of the equations is valid for the circuit below?
A) 2 – I1 – 2I2 = 0
B) 2 – 2I1 – 2I2 – 4I3 = 0
C) 2 – I1 – 4 – 2I2 = 0
D) I3 – 4 – 2I2 + 6 = 0
E) 2 – I1 – 3I3 – 6 = 0
Conceptual questions
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+
+
+
9 V
9 V
9 V
ΔVab if one battery is reversed?
a
b
ΔVab= 27V
Δvab= 9v
quiz
Calculate ΔVab
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AI 625.0
quiz
Calculate the current in the circuit.
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Find the current I, r and ε.
I = 3 Ar =2 =-5 V
quiz
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Calculate the currents I1, I2, and I3 in the three branches of the circuit in the figure.
Quiz
I1 = - 0.87 A. I2 = 2.6 A. I3 = 1.7 A.
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summary
Kirchhoff’s Rules
outin II1-
2- Loop Rule
Series combination: 321 RRRRs
Parallel combination 1111
321
RRRRp
0i
iV
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Home work 45,46,71