Physics 212 Lecture 10, Slide 1

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Physics 212 Lecture 10
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Music

• Who is the Artist?
• Miles Davis
• Wynton Marsalis
• Chris Botti
• Nina Simone
• Chet Baker

Why? THE DEFINITIVE My Funny Valentine Happy
Valentines Day !!
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Things you identified as difficult
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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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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.
Your height about the ground is your potential.
No matter how many stairs you go up and elevators
you go down or vice versa, if you end up in the
same place you started, you still are at the same
height and therefore have the same potential.
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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.
The amount of water that enters a pipe must be
exactly equal to the amount of water that leaves
the pipe. This is true even if water enters a
connection of pipes through one pipe and leaves
through three pipes. The amount of water is the
same because we can assume there is no leak. This
is the same idea with Kirchoff's Current Rule, we
assume there exist no current leaks.
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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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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
12
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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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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Last Time

• V 18V
• R1 1W
• R2 2W
• R3 3W
• R4 4W.
• R24 6W
• R234 2W
• Vab 12V
• V2 4V

R2
R1
V

R3
R4

• Where to start?
• Make the change to the circuit and see how that
  changes everything else!
• R24 decreases ( 6W ? 2W)
• R234 decreases ( 2W ? 1.2W)
• Do the math or consider limit (R24 ? 0 ?
  R234 ? 0 )
• I1 increases (6A 8.2A)
• R234 decreases ? R1 R234 decreases ?
  I1 increases

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One More Question

• V 18V
• R1 1W
• R2 2W
• R3 3W
• R4 4W. ? 0
• R24 6W ? 2W
• R234 2W ? 1.2W
• Vab 12V
• V2 4V

R2
R1
V

R3
R4

• Why?
• We know I1 increases (6A ? 8.2A)
• V3 must therefore decrease (12V ? 9.8V)
• Increased I1 increases V1 (V1 I1R1), but V3
  V V1
• I3 must therefore also decrease since I3
  V3/R3

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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

• 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
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
• 1 node equation
• 2 loop 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??
• (D) is an attempt to write down KVR for the top
  loop
• Start at negative terminal of V2 and go clockwise
• Vgain (-V2) then Vgain (-I2R2) then Vgain
  (-I1R1) then Vdrop (V1)

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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

• We have the following 4 equations

We need 3 equations Which 3 should we use?
1. I2 I1 I3 2. - V1 I1R1
- I3R3 V3 0 3. - V3 I3R3 I2R2 V2
0 4. - V2 I2R2 - I1R1 V1 0
A) Any 3 will do B) 1, 2, and
4 C) 2, 3, and 4

• Why??
• We need 3 INDEPENDENT equations
• Equations 2, 3, and 4 are NOT INDEPENDENT
• Eqn 2 Eqn 3 - Eqn 4
• We must choose Equation 1 and any two of the
  remaining ( 2, 3, and 4)

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Calculation Simplify
V1
R1
I1
In this circuit, assume Vi and Ri are
known. What is I2 ??
V2
R2
I2
R3
V3
I3

• We have 3 equations and 3 unknowns.
• The solution will get very messy!
• Simplify assume V2 V3 V
• V1 2V
• R1 R3 R
• R2 2R

• With this simplification, you can verify
• I2 ( 1/5) V/R
• I1 ( 3/5) V/R
• I3 (-2/5) V/R

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Follow-Up

• We know
• I2 ( 1/5) V/R
• I1 ( 3/5) V/R
• I3 (-2/5) V/R

a
b
Why? Redraw
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R