Physics 212 Lecture 9, Slide 1

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Physics 212 Lecture 9
Today's Concept Electric Current Ohms Law
resistors Resistors in circuits Power in circuits
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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.
3
Thanks for your feedback about the course
Based on these, we will try the following
today 1) Summary of the important concepts to
learn in each lecture 2) Make sure we have time
to work out the problem all the way
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Key Concepts

• How resistance depends on A, L, s, r
• How to combine resistors in series and parallel
• Understanding resistors in circuits

Todays Plan

• Review of resistance preflights
• Work out a circuit problem in detail
• Optional Comments on drift velocity average
  velocity
• - How do these charges move anyway?

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I
A
s
L
V
J s E
same as
I V/R
L
R
where
sA
6
R
I
V
I V/R
Ohms Law
Aside Q What is a battery ? A A device that
produces a potential difference V between
its two terminals !
(aka EMF)
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This is just like plumbing! I is
like flow rate of water V is like pressure R is
how hard it is for water to flow in a pipe
To make R big, make L long or A small
To make R small, make L short or A big
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A B C
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Preflight 2
VIR and R2 has lower resistance because of its
larger area.
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Preflight 4
Since I is the same in both, R is proportional to
V. Since R2 is bigger, V2 must also be bigger.
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Preflight 6
Current is always the same in series since it has
only one path to travel.
12
Preflight 8
R2 is a third of the total resistance, therefore
V2 will be a third of the total voltage E.
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Resistor Summary
Series
Parallel
R1
R2
R1
R2
Each resistor on the same wire.
Each resistor on a different wire.
Wiring
Different for each resistor. Vtotal V1 V2
Same for each resistor. Vtotal V1 V2
Voltage
Same for each resistor Itotal I1 I2
Different for each resistor Itotal I1 I2
Current
Increases Req R1 R2
Decreases 1/Req 1/R1 1/R2
Resistance
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Calculation
R2
R1

• In the circuit shown V 18V,
• R1 1W, R2 2W, R3 3W, and R4 4W.
• What is V2, the voltage across R2?

V
R3
R4

• Conceptual Analysis
• Ohms Law when current I flows through
  resistance R, the potential drop V is given by V
  IR.
• Resistances are combined in series and parallel
  combinations
• Rseries Ra Rb
• (1/Rparallel) (1/Ra) (1/Rb)
• Strategic Analysis
• Combine resistances to form equivalent
  resistances
• Evaluate voltages or currents from Ohms Law
• Expand circuit back using knowledge of voltages
  and currents

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Calculation
R2
R1

• In the circuit shown V 18V,
• R1 1W, R2 2W, R3 3W, and R4 4W.
• What is V2, the voltage across R2?

V
R3
R4

• Combine Resistances

Parallel Can make a loop that contains only
those two resistors Series Every loop with
resistor 1 also has resistor 2.
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Calculation
R2
R1

• In the circuit shown V 18V,
• R1 1W, R2 2W, R3 3W, and R4 4W.
• What is V2, the voltage across R2?

V
R3
R4

• Combine Resistances

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Calculation
R2
R1

• In the circuit shown V 18V,
• R1 1W, R2 2W, R3 3W, and R4 4W.
• What is V2, the voltage across R2?

V
R3
R4

• Combine Resistances

R2 and R4 are connected in series R24 2 4
6 W
Redraw the circuit using the equivalent resistor
R24 series combination of R2 and R4.
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Calculation

• In the circuit shown V 18V,
• R1 1W, R2 2W, R3 3W, and R4 4W.
• R24 6W
• What is V2, the voltage across R2?

• Combine Resistances

R2 and R4 are connected in series R24 R3 and
R24 are connected in parallel R234
(1/Rparallel) (1/Ra) (1/Rb)
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Calculation
R1

• In the circuit shown V 18V,
• R1 1W, R2 2W, R3 3W, and R4 4W.
• R24 6W R234 2W
• What is V2, the voltage across R2?

V
I1 I234
R234
R1 and R234 are in series. R1234 1 2 3 W
V
R1234
I1234
Ohms Law tells us I1234 V/R1234
18 / 3
6 Amps
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Calculation
V

• In the circuit shown V 18V,
• R1 1W, R2 2W, R3 3W, and R4 4W.
• R24 6W R234 2W I1234 6 A
• What is V2, the voltage across R2?

I1234
R1234
R1

I234 I1234 Since R1 in series w/ R234
V
R234
V234 I234 R234 6 x 2
12 Volts
I1 I234

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Calculation

• V 18V
• R1 1W
• R2 2W
• R3 3W
• R4 4W.
• R24 6W
• R234 2W
• I1234 6 Amps
• I234 6 Amps
• V234 12V
• What is V2?

Which of the following are true? A) V234 V24 B)
I234 I24 C) Both AB D) None
Since R3 and R24 where combined in parallel to
get R234 Voltages are same!
Ohms Law I24 V24 / R24 12 / 6
2 Amps
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Calculation

• V 18V
• R1 1W
• R2 2W
• R3 3W
• R4 4W.
• R24 6W
• R234 2W
• I1234 6 Amps
• I234 6 Amps
• V234 12V
• V24 12V
• I24 2 Amps
• What is V2?

Which of the following are true? A) V24 V2 B)
I24 I2 C) Both AB D) None
Since R2 and R4 where combined in series to get
R24 Currents are same!
Ohms Law V2 I2 R2 2 x 2 4
Volts!
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If the electric field is always zero inside an
ideal conductor
then this implies that the charges can rearrange
themselves instantaneously when an external
electric field is applied
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E
E 0
If the electric field is always zero inside an
ideal conductor
then this implies that the charges can rearrange
themselves instantaneously when an external
electric field is applied
Real life is not so boring
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I
area A
E
vave
When an electric field is applied in most
materials ,the charges flowwith a finite vave
and the electric field inside the material is not
zero
I
J s E
A
Current density
Conductivity
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Why talk about Current Density J I / A ??
2I
area 2A
E
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I JA
area A
I
E
vave
L
r charge density Q/Volume ( eNe)
Suppose
JA
I Arvave
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J s E
This equation contains the actual physics, but in
a practical circuit we measure voltage
differences DV and currents I
DV EL
I
J s E
A
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If 5 gallons of water per minute are flowing
throughboth of the pipes shown, in which pipe is
the water moving fastest ?
CD

• The skinny pipe
• The fat pipe
• They are the same