Circuits and Ohms Law

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Circuits and Ohms Law
Physics 102 Lecture 05
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Summary of Last Time

• Capacitors
• Physical C e0A/d CQ/V
• Series 1/Ceq 1/C1 1/C2
• Parallel Ceq C1 C2
• Energy U 1/2 QV

Summary of Today

• Resistors
• Physical R r L/A VIR
• Series Req R1 R2
• Parallel 1/Req 1/R1 1/R2
• Power P IV

5
3
Electric Terminology

• Current Moving Charges
• Symbol I
• Unit Amp ? Coulomb/second
• Count number of charges which pass point/sec
• Direction of current is direction that flows
• Power Energy/Time
• Symbol P
• Unit Watt ? Joule/second Volt Coulomb/sec
• P VI

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4
Physical Resistor

• Resistance Traveling through a resistor,
  electrons bump into things which slows them down.
  R r L /A
• r Resistivity Density of bumps
• L Length of resistor
• A Cross sectional area of resistor
• Ohms Law I V/R
• Cause and effect (sort of like aF/m)
• potential difference cause current to flow
• resistance regulate the amount of flow
• Double potential difference ? double current
• I (VA)/ (r L)

A
L
10
5
Preflight 5.1

• Two cylindrical resistors are made from the same
  material. They are of equal length but one has
  twice the diameter of the other.
• R1 gt R2
• R1 R2
• R1 lt R2

The greater the area, the easier it is for
current to flow through
72 5 24
The charge has to travel the same distance in
each resistor
The bigger the resistor, the greater the
resistance.
R r L /A
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ComparisonCapacitors vs. Resistors

• Capacitors store energy as separated charge
  UQV/2
• Capacitance ability to store separated charge
  C ke0A/d
• Voltage drop determines charge VQ/C
• Resistors dissipate energy as power PVI
• Resistance how difficult it is for charges to
  get through R r L /A
• Voltage drop determines current VIR
• Dont mix capacitor and resistor equations!

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Simple Circuit
Example
I
e

• Visualization
• Practice
• Calculate I when e24 Volts and R 8 W
• Ohms Law V IR

R
I
I V/R
3 Amps
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Resistors in Series

• One wire
• Effectively adding lengths
• Reqr(L1L2)/A
• Since R a L add resistance
• Visualization

Req R1 R2
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Resistors in SeriesProof that ReqR1R2

• Resistors connected end-to-end
• If charge goes through one resistor, it must go
  through other.
• I1 I2 Ieq
• Both have voltage drops
• V1 V2 Veq

R1
Req
R2
Req Veq V1 V2 R1 R2
Ieq Ieq
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Preflight 5.3

• Compare I1 the current through R1, with I10 the
  current through R10.
• I1ltI10
• I1I10
• I1gtI10

11 67 22
Since they are connected in series, the current
is the same for every resistor. If charge goes
through one resistor, it must go through other.
Note I is the same everywhere in this circuit!
ACT Series Circuit
Compare V1 the voltage across R1, with V10 the
voltage across R10. 1. V1gtV10 2. V1V10 3. V1ltV10
V1 I1 R1 I x 1 V10 I10 R10 I x 10
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PracticeResistors in Series
Example

• Calculate the voltage across each resistor if the
  battery has potential V0 22 volts.

• R12 R1 R2
• V12 V1 V2
• I12 I1 I2

Simplify (R1 and R2 in series)
11 W
V0 22 Volts
V12/R12 2 Amps

• Expand
• V1 I1R1
• V2 I2R2

2 x 1 2 Volts
2 x 10 20 Volts
Check V1 V2 V12 ?
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Resistors in Parallel

• Two wires
• Effectively adding the Area
• Since R a 1/A add 1/R

Visualization
1/Req 1/R1 1/R2


R
R/2
R
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Resistors in Parallel

• Both ends of resistor are connected
• Current is split between two wires
• I1 I2 Ieq
• Voltage is same across each
• V1 V2 Veq

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Preflight 5.5

• What happens to the current through R2 when the
  switch is closed?
• Increases
• Remains Same
• Decreases

36 26 38
ACT Parallel Circuit
What happens to the current through the
battery? (1) Increases (2) Remains
Same (3) Decreases
Ibattery I2 I3
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Practice Resistors in Parallel
Example

• Determine the current through the battery.
• Let E 60 Volts, R2 20 W and R330 W.

Simplify R2 and R3 are in parallel
1/R23 1/R2 1/R3 V23 V2 V3 I23 I2 I3
R23 12 W
60 Volts
V23 /R23 5 Amps
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ACT Your Kitchen
Johnny Danger Powells uses one power strip to
plug in his microwave, coffee pot, space heater,
toaster, and guitar amplifier all into one outlet.
Toaster
This is dangerous because (By the way, power
strips are wired in parallel.)
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Summary
Series
Parallel
R1
R1
R2
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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ACT/Preflight 5.6, 5.7
1
2
3
R 2R R/2

• Which configuration has the smallest resistance?
• 1
• 2
• 3

26 5 69
The one has only one resistor so it has the
least resistance
In parallel, the resistors add like this (1/R)
(1/R)-1 which is the same as R/2. This means
the resistance is halved compared to a single R.
In series, the total resistance is just R R or
2R, twice the resistance of A.
Which configuration has the largest
resistance? 2 80 Nice Work!
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Parallel Series Tests

• Resistors R1 and R2 are in series if and only if
  every loop that contains R1 also contains R2
• Resistors R1 and R2 are in parallel if and only
  if you can make a loop that has ONLY R1 and R2
• Same rules apply to capacitors!!

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Try it!
Example
R1
e
R2
R3
Calculate current through each resistor. R1 10
W, R2 20 W, R3 30 W, e44 V

• Simplify R2 and R3 are in parallel
• 1/R23 1/R2 1/R3
• V23 V2 V3
• I23 I2 I3

R1
R23 12 W
e
R23

• Simplify R1 and R23 are in series
• R123 R1 R23
• V123 V1 V23 e
• I123 I1 I23 Ibattery

R123 22 W
e
R123
I123 44 V/22 W 2 A
Power delivered by battery?
PIV 2?44 88W
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Try it! (cont.)
Example
Calculate current through each resistor. R1 10
W, R2 20 W, R3 30 W, e44 V

• Expand R1 and R23 are in series
• R123 R1 R23
• V123 V1 V23 e
• I123 I1 I23 Ibattery

I23 2 A
V23 I23 R23 24 V

• Expand R2 and R3 are in parallel
• 1/R23 1/R2 1/R3
• V23 V2 V3
• I23 I2 I3

I2 V2/R2 24/201.2A
e
I3 V3/R3 24/300.8A
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See you next Monday!

• Read 18.5, 18.7
• Extra Problems from Ch 18
• Conceptual 9
• Multiple Choice 4
• Problems 24, 25, 40, 41, 42