Physics 2112
Unit 10: Kirchhoff’s Rules
Today’s Concept:
Kirchhoff’s Rules
Electricity & Magnetism Lecture 10, Slide 1
Kirchhoff’s Laws: Why use them?
R1
R3
V1
V2
R2
How Can We Solve This One?
R1
R3
V1
V2
R2
=
V
I1234
R12
THE ANSWER: Kirchhoff’s Rules
Electricity & Magnetism Lecture 10, Slide 2
Based on two concepts
 V = 0
i
Kirchhoff's Voltage Rule states that the sum of the voltage
changes caused by any elements (like wires, batteries, and
resistors) around a circuit must be zero.
I
in
=  I out
Kirchhoff's Current Rule states that the sum of all currents
entering any given point in a circuit must equal the sum of all
currents leaving the same point.
Electricity & Magnetism Lecture 10, Slide 3
Two Ways to do the algebra
R1
V1
I1
R1
R3
V2
R3
I3 V 1
I2
R2
Method #1
current in every leg
3 equations,
3 unknowns
I1
I2
R2
V2
Method #2
“current” in every loop
2 equations,
2 unknowns
Electricity & Magnetism Lecture 10, Slide 4
We will use second method
1) Choose loops and direction
Place “current” in each one
2) Write down voltage drops and
gains
3) Across a battery: – to + is a
voltage gain, + to – is a drop
4) Across a resistor: with the
current is a voltage drop,
against the current voltage
gain
A
-
+
+
+
R2
+
E1
-
B
I1
E3
I2
-
+
E2
-
R3
R5
-
I3
+
+
R4
+
I5
Electricity & Magnetism Lecture 10, Slide 5
Choosing Loops
Doesn’t as long as every element is
in at least one loop
A
-
+
+
+
R2
+
E1
-
B
I1
E3
-
-
I2
-
+
E2
A
R3
R5
-
I3
+
+
-
+
-
+
+
+
R2
+
E1
-
B
I1
E3
-
-
R4
R3
R5
I5
-
I2
+
E2
I3
-
+
+
+
I5
Electricity & Magnetism Lecture 10, Slide 6
CheckPoint: Gains and Drops
In the following circuit, consider the loop abc. The direction of the current through each resistor is indicated
by black arrows.
If we are to write Kirchhoff's voltage equation for this loop in the clockwise direction starting from point a,
what is the correct order of voltage gains/drops that we will encounter for resistors R1, R2 and R3?
a)
b)
c)
d)
e)
drop, drop, drop
gain, gain, gain
drop, gain, gain
gain, drop, drop
drop, drop, gain
Electricity & Magnetism Lecture 10, Slide 7
Example 10.1
1
2
2V
1V
1
In this circuit, assume Vi and Ri are known.
IM
What is IM ?
1V
Conceptual Analysis:
–
Circuit behavior described by Kirchhoff’s Rules:
• KVR: S Vdrops = 0
Strategic Analysis
–
–
Write down Loop Equations (KVR)
Solve
Electricity & Magnetism Lecture 10, Slide 8
Calculation
1
2
1
2V
Choose Loops and put
currents in them.
1V
I2
1V
Electricity & Magnetism Lecture 10, Slide 9
Example 10.2
I2
4=R1
6=R3
12V
In this circuit, what is the current o
battery ?
I1
3=R2
Conceptual Analysis:
–
Circuit behavior described by Kirchhoff’s Rules:
• KVR: S Vdrops = 0
Strategic Analysis
–
–
Write down Loop Equations (KVR)
Solve
Electricity & Magnetism Lecture 10, Slide 10
Redraw circuit
4=R1
6=R3
12V
3=R2
3=R2
6=R3
12V
4=R1
Electricity & Magnetism Lecture 10, Slide 11
CheckPoint: Circuits w/ Resistors and a Battery 1
Consider the circuit shown below. Which of the following
statements best describes the current flowing in the blue wire
connecting points a and b?
A. Positive current flows from a to b
B. Positive current flows from b to a
C. No current flows between a and b
Electricity & Magnetism Lecture 10, Slide 12
Prelecture
What is the same?
CheckPoint
Current flowing in and out of the battery.
2R
3
2R
3
What is different?
Current flowing from a to b.
Electricity & Magnetism Lecture 10, Slide 13
I
2/
3I
R
1/
3I
a
V
2/
2/ I
3
3I
b
R
1/
3I
V/2
2R
1/
1/
03I
12/ I
3
2R
1/
3I
2/
3I
3I
Electricity & Magnetism Lecture 10, Slide 14
CheckPoint: Circuits w/ Resistors and a Battery 2
Consider the circuit shown below. In which case is the current flowing in the blue wire
connecting points a and b bigger?
(A) Case A
(B) Case B
(C)They are the same
Electricity & Magnetism Lecture 10, Slide 15
Parallel and Series (with color)
R1
R2
V
R3
R4
If every electron that goes
through one element must go
through another, those two are
in series.
If two sides of two elements can
be connected by different
colored lines, those two are in
parallel. .
If two points are connected by a line not
containing any circuit elements those point are at
the same potential.
Unit 9, Slide 16
Example 10.3
0.1
3V
2
2
A battery has an EMF of
3V and an internal
resistance of 0.1. It is
hooked in parallel to two
light bulbs which both
that a resistance of 2
when hot.
What would a voltmeter read if it was connected to
across the terminals of the battery when
a) Both switches were open?
b) When one switch is closed?
c) When both switches are closed?
Unit 10, Slide 17