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