Physics 2112Unit 10: Kirchhoff’s Rules
Today’s Concept:Kirchhoff’s Rules
Electricity & Magnetism Lecture 10, Slide 1
THE ANSWER: Kirchhoff’s Rules
VR12
I1234=V1
R1
R2V2
R3
How Can We Solve This One?
V1
R1
R2V2
R3
I1234
Kirchhoff’s Laws: Why use them?
Electricity & Magnetism Lecture 10, Slide 2
Based on two concepts
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.
Electricity & Magnetism Lecture 10, Slide 3
0iV
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.
outin II
Method #1
current in every leg
3 equations, 3 unknowns
V1
R1
R2
V2
R3
Two Ways to do the algebra
Electricity & Magnetism Lecture 10, Slide 4
V1
R1
R2V2
R3I1I2
I3
Method #2
“current” in every loop
2 equations, 2 unknowns
I1 I2
We will use second method
1) Choose loops and directionPlace “current” in each one
2) Write down voltage drops and gains
R4
+
+
+ +
+
-
-
-
-
-
+
+
+
-
-
-
E1
R2
R3E2
E3
R5
A
B3) Across a battery: – to + is a voltage gain, + to – is a drop
I5
Electricity & Magnetism Lecture 10, Slide 5
I1 I2
I3
4) Across a resistor: with the current is a voltage drop, against the current voltage gain
Choosing Loops
Doesn’t as long as every element is in at least one loop
R4
Electricity & Magnetism Lecture 10, Slide 6
+
+
+ +
+
-
-
-
-
-
+
+
+
-
-
-
E1
R2
R3E2
E3
R5
A
B
I5
I1 I2
I3
+
+
+ +
+
-
-
-
-
-
+
+
+
-
-
-
E1
R2
R3E2
E3
R5
A
B
I5
I1 I2
I3
CheckPoint: Gains and Drops
Electricity & Magnetism Lecture 10, Slide 7
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) drop, drop, dropb) gain, gain, gainc) drop, gain, gaind) gain, drop, drope) drop, drop, gain
2V
1V
1V
Conceptual Analysis: – Circuit behavior described by Kirchhoff’s Rules:
• KVR: S Vdrops = 0
Strategic Analysis– Write down Loop Equations (KVR)– Solve
IM
Example 10.1
1
2
1
In this circuit, assume Vi and Ri are known.
What is IM ?
Electricity & Magnetism Lecture 10, Slide 8
Calculation
Electricity & Magnetism Lecture 10, Slide 9
2V
1V
1V
1
2
1 I2
Choose Loops and put currents in them.
12V
Conceptual Analysis: – Circuit behavior described by Kirchhoff’s Rules:
• KVR: S Vdrops = 0
Strategic Analysis– Write down Loop Equations (KVR)– Solve
Example 10.2
In this circuit, what is the current out of the battery ?
Electricity & Magnetism Lecture 10, Slide 10
4W=R1
3W=R2
6W=R3
I2
I1
12V
Redraw circuit
Electricity & Magnetism Lecture 10, Slide 11
4W=R1
3W=R2
6W=R3
12V
3W=R26W=R3
4W=R1
CheckPoint: Circuits w/ Resistors and a Battery 1
Electricity & Magnetism Lecture 10, Slide 12
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 bB. Positive current flows from b to aC. No current flows between a and b
What is the same? Current flowing in and out of the battery.
What is different? Current flowing from a to b.
2R3
2R3
Prelecture CheckPoint
Electricity & Magnetism Lecture 10, Slide 13
2RI1/3
R2/3I
V
R 2R
a b
I2/3I
V/2
I
1/3
0
2/3I
2/3I
2/3I
1/3I
1/3I
1/3I
2/3I1/3I
Electricity & Magnetism Lecture 10, Slide 14
CheckPoint: Circuits w/ Resistors and a Battery 2
Electricity & Magnetism Lecture 10, Slide 15
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
Parallel and Series (with color)
Unit 9, Slide 16
V
R1 R2
R4R3
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.
Example 10.3
Unit 10, Slide 17
3V
A battery has an EMF of 3V and an internal resistance of 0.1W. It is hooked in parallel to two light bulbs which both that a resistance of 2W 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?
2W 2W0.1W
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