1. Physics 2112 Unit 10: Kirchhoff’s Rules
Today’s Concept:
Kirchhoff’s Rules

2. Kirchhoff’s Laws: Why use them?
How Can We Solve This One? V1 R1 R2 V2 R3 V
R12
I1234 = V1 R1 R2 V2 R3
I1234
THE ANSWER: Kirchhoff’s Rules

3. 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.
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.

4. Two Ways to do the algebraV1 R1 R2 V2 R3 V1 R1 R2 V2 R3 I1 I3 I2 I1 I2
Method #2
“current” in every loop
2 equations, 2 unknowns
Method #1
current in every leg
3 equations, 3 unknowns

5. We will use second method
Choose loops and direction
Place “current” in each one
2) Write down voltage drops and gains A + - + - R2 E3
3) Across a battery: – to + is a voltage gain, + to – is a drop B I1 I2 E1 I3 R3 R4 E2
4) Across a resistor: with the current is a voltage drop, against the current voltage gain R5 I5
Have students label I5, since it isn’t shown in their drawing

6. Doesn’t as long as every element is in at least one loop
Choosing Loops
Doesn’t as long as every element is in at least one loop + - E1 R2 R3 E2 E3 R5 A B I5 I1 I2 I3 + - E1 R2 R3 E2 E3 R5 A B I5 I1 I2 I3 R4
Have students label I5, since it isn’t shown in their drawing

7. 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?
Have students label I5, since it isn’t shown in their drawing
drop, drop, drop
gain, gain, gain
drop, gain, gain
gain, drop, drop
drop, drop, gain

8. In this circuit, assume Vi and Ri are known.
Example 10.1 2V
In this circuit, assume Vi and Ri are known.
What is IM ? 1V IM 1V
Conceptual Analysis:
Circuit behavior described by Kirchhoff’s Rules:
KVR: S Vdrops = 0
Strategic Analysis
Write down Loop Equations (KVR)
Solve

9. Choose Loops and put currents in them.
Calculation 2V
Choose Loops and put currents in them. 1V I2 1V
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.

10. In this circuit, what is the current out of the battery ?
Example 10.2 I2
6W=R3
4W=R1
12V
In this circuit, what is the current out of the battery ? I1
3W=R2
Conceptual Analysis:
Circuit behavior described by Kirchhoff’s Rules:
KVR: S Vdrops = 0
Strategic Analysis
Write down Loop Equations (KVR)
Solve

11. Redraw circuit
6W=R3
4W=R1
12V
3W=R2
12V
3W=R2
6W=R3
4W=R1

12. 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?
Positive current flows from a to b
Positive current flows from b to a
No current flows between a and b
Have students label I5, since it isn’t shown in their drawing

13. Prelecture CheckPoint
What is the same? Current flowing in and out of the battery. 2R 3
What is different? Current flowing from a to b.

14. 2R I
1/3 R
2/3I V a b
V/2
1/3I

15. 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
Have students label I5, since it isn’t shown in their drawing

16. Parallel and Series (with color)V R1 R2 R4 R3
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.

17. Example 10.3
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.
0.1W 2W 2W 3V
What would a voltmeter read if it was connected to across the terminals of the battery when
Both switches were open?
When one switch is closed?
When both switches are closed?