Physics 212 Lecture 10, Slide 1

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Physics 212 Lecture 10
Today's Concept Kirchhoffs Rules Circuits
with resistors batteries
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Your Thoughts
The blue wire questions are killing my buzz.
I'm not really clear on applying the rules. Like
problem 6 above, I don't know how to do that one
what are those zigzag lines on pictures?
This whole blue wire concept - I'm not sure I got
it right.
Nothing, I'm good with Kirchov's laws (aside from
spelling that name)
Kirchoff's Current Rule is still confusing to me,
and another example of how to apply it would
really help.
How do you deal with a capacitor in a circuit of
resistors and batteries.
The reason that Skynet and the terminators
survive after an EMP is becasue they go into
automatic reboot on their shielded battery power.
Then they rebuild from there, like sea monkeys on
a sea banana trees.
What would happen if they discovered one day that
everything we thought we knew about physics was
completely wrong, and Newton and all those guys
were just really close to the truth, but still
wrong. Would we still have to finish the class? I
mean there's no sense learning stuff thats not
true anymore..... maybe that means everyone would
get an A on midterm 1, or an F. I dont really
know what I'm talking about. It would be funny if
this got posted on the overhead before class as
one of those nonsense responses from the
prelectures..
My friend went to the review session and noticed
that you look a lot like a younger version of
someone in a movie. Just to see if he is right,
could you say "Welcome to Jurassic Park!"
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How confident are you in your understanding of
the concepts presented in the prelecture? A  I
am confused by all of it. B  I understand a
little but I am confused by most of it. C  I
understand some parts and I am confused by other
parts. D  I understand most of itE  I
understand everything F I didn't view the whole
prelecture so I can't comment.
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Key Concepts

• Understanding Kirchoffs Rules
• Using Kirchoffs Rules

Todays Plan

• Comment on real batteries
• Summary of Kirchoffs rules
• Example problem
• Review Preflights

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A quick comment on Batteries

r
VL
R
V0
Usually cant supply too much current to the load
without voltage sagging
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Consider a thin AAA battery and a fat D-Cell
battery.
Which battery has a larger potential difference
(unloaded) A) AAA B) Same C) D-Cell
Which battery has more energy (when new)? A)
AAA B) Same C) D-Cell
Which battery would you model having a larger
r? A) AAA B) Same C) D-Cell
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AAA
D
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Last Time
Resistors in series
Current thru is same Voltage drop across is
IRi
Last Lecture
Resistors in parallel
Voltage drop across is same Current thru is
V/Ri
Solved Circuits
Today
What about this one?
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Kirchoffs Voltage Rule
Kirchoff'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. If we model voltage as height above
the ground floor, see if you can come up with the
analogy to Kirchoff's Voltage Rule in terms of
someone walking around in the hallways and
stairways and elevators of a high-rise building.
If we start at the ground floor with a potential
of 0, and walk around up and down stairs, take
the elevator a few flights, go to the roof,
parachute off, and end up back on the ground
floor, our potential is still 0. Therefore, the
potential difference is 0. We may have increased
and decreased our potential as we traveled
through the building, but we still start and end
at a potential of 0. Gotta love conservative
forces!!
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Kirchoffs Current Rule
Kirchoff'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. If we model electrical
current as water, see if you can come up with an
analogy to Kirchoff's Current Rule in terms of
household plumbing.
If you have a main water line coming into your
house, it will split off to service all
utilities, such as sink, toilet, shower, etc. The
water in all of those lines must equal the amount
of water coming out of the main line, and when
all the household water drains out of the house
into a main line again, all the smaller lines
must include as much water as the drain carries
out.
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a
b
CD
V
R
R

• Is there a current flowing between a and b ?
• Yes
• No

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Kirchhoffs Laws
(1) Label all currents Choose any direction
(2) Label /- for all elements Current goes ?
- (for resistors)

• Choose loop and direction
• Must start on wire, not element.

R4

• Write down voltage drops
• First sign you hit is sign to use.

• Write down node equation Iin Iout

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Calculation
2V
In this circuit, assume Vi and Ri are
known. What is I2 ??
1V
I2
1V

• Conceptual Analysis
• Circuit behavior described by Kirchhoffs Rules
  
• KVR SVdrops 0
• KCR SIin SIout
• Strategic Analysis
• Write down Loop Equations (KVR)
• Write down Node Equations (KCR)
• Solve

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Calculation
V1
R1
In this circuit, assume Vi and Ri are
known. What is I2 ??
V2
R2
R3
V3
Label the and side of each element
Now write down loop and node equations
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Calculation
V1
R1
I1
-
-
In this circuit, assume Vi and Ri are
known. What is I2 ??
V2
R2
I2
-
-
R3
V3
I3
-
-

• Why??
• We have 3 unknowns I1, I2, and I3
• We need 3 independent equations to solve for
  these unknowns

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Calculation
V1
R1
I1
-
-
In this circuit, assume Vi and Ri are
known. What is I2 ??
V2
R2
I2
-
-
R3
V3
I3
-
-
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Calculation
V1
R1
I1
-
-
In this circuit, assume Vi and Ri are
known. What is I2 ??
V2
R2
I2
-
-
R3
V3
I3
-
-
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Calculation
V1
R1
I1
-
-
In this circuit, assume Vi and Ri are
known. What is I2 ??
V2
R2
I2
-
-
R3
V3
I3
-
-
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V1
R1
I1
-
-
I3 I1 I2 0
V2
R2
I2
V2 - V3 I3R3 I2R2 0
-
-
R3
V3
I3
- V1 I1R1 - I3R3 V3 0
-
-
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V - V I3R 2I2R 0
- 2V I1R - I3R V 0
I3 I1 I2 0
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Prelecture
Preflight
Things that are the same Current flowing in and
out of the battery Currents and voltages for
all resistors
Things that are different Current flowing from
a to b
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R
2R
V
a
b
V/2
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R
2R
V
a
b
V/2
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I
I
1/3
2/3I
R
2R
V
a
b
V/2
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R
V
a
b
V/2
Another way to see this
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CD
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