Transcript Circuits and Ohm`s Law

Physics 102: Lecture 05
Circuits and Ohm’s Law
• Today’s lecture will cover Textbook
sections 18.4,.6, 8
Practice exams available on course webpage
under “Course Info”
Homework, keep lots of digits!
Physics 102: Lecture 5, Slide 1
Last Time
• Capacitors
–
–
–
–
Physical
Series
Parallel
Energy
C = e0A/d
1/Ceq = 1/C1 + 1/C2
Ceq = C1 + C2
U = 1/2 QV
Today
• Resistors
–
–
–
–
Physical
Series
Parallel
Power
Physics 102: Lecture 5, Slide 2
R = r L/A
Req = R1 + R2
1/Req = 1/R1 + 1/R2
P = IV
Electric Terminology
• Current: Moving Charges
– Symbol: I
– Unit: Amp  Coulomb/second
– Count number of charges which pass point/sec
• Power: Energy/Time
– Symbol: P
– Unit: Watt  Joule/second = Volt Coulomb/sec
– P = IV
Physics 102: Lecture 5, Slide 3
Physical Resistor
• Resistance: Traveling through a resistor,
electrons bump into things which slows
them down. R = r L /A
A
– r:
– L:
– A:
L
• Ohms Law I = V/R
– Double potential difference  double current
Physics 102: Lecture 5, Slide 4
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.
1.
R1 > R2
2.
R1 = R2
3.
R1 < R2
Physics 102: Lecture 5, Slide 5
1
2
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.
1.
R1 > R2
2.
R1 = R2
3.
R1 < R2
Physics 102: Lecture 5, Slide 6
R = ρ L/A
1
2
Comparison:
Capacitors vs. Resistors
• Capacitors store energy as separated charge: U=1/2QV
– Capacitance: ability to store separated charge:
C = ke0A/d
– Voltage determines charge: V=Q/C
• Resistors dissipate energy as power: P=VI
– Resistance: how difficult it is for charges to get through:
R = r L /A
– Voltage determines current: V=IR
• Don’t mix capacitor and resistor equations!
Physics 102: Lecture 5, Slide 7
Simple Circuit
I
e
• Practice…
R
I
– Calculate I when e = 24 Volts and R = 8 W
Physics 102: Lecture 5, Slide 8
Simple Circuit
I
• Visualization
• Practice…
e
– Calculate I when e=24 Volts and R = 8 W
– Ohm’s Law: V =IR
I = V/R
Physics 102: Lecture 5, Slide 9
= 3 Amps
R
I
Resistors in Series
• One wire:
– Effectively adding lengths:
• Req=r(L1+L2)/A
– Since R  L, add resistance:
R
=
Req = R1 + R2
R
Physics 102: Lecture 5, Slide 10
2R
Resistors in Series
• Resistors connected end-to-end:
– If current goes through one resistor, it
must go through other.
I1 = I2 = Ieq
– Both have voltage drops:
V1 + V2 = Veq
Req = Veq = V1 + V2 = R1 + R2
Ieq
Ieq
Physics 102: Lecture 5, Slide 11
R1
Req
R2
Preflight 5.3
Compare I1 the current through R1, with
I10 the current through R10.
1.
I1 < I10
2.
I1 = I10
3.
I1 > I10
R1=1W
e
0
R10=10W
ACT: Series Circuit
Compare V1 the voltage across R1, with V10 the voltage across R10.
1. V1>V10
Physics 102: Lecture 5, Slide 12
2. V1=V10
3. V1<V10
Preflight 5.3
R1=1W
Compare I1 the current through R1, with
I10 the current through R10.
1.
I1<I10
2.
I1=I10
3.
I1>I10
e
0
R10=10W
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. V1>V10
2. V1=V10
3. V1<V10
Physics 102: Lecture 5, Slide 13
V1 = I1 R1 = 1 x I
V10 = I10 R10 = 10 x I
Practice:
Resistors in Series
R1=1W
e0
R2=10W
Calculate the voltage across each resistor if
the battery has potential V0 = 22 volts.
Simplify (R1 and R2 in series):
• R12 =
• V12 =
• I12 =
e0
R12
Expand:
•V1 =
•V2 =
Check: V1 + V2 = V12 ?
Physics 102: Lecture 5, Slide 14
R1=1W
e0
R2=10W
Practice:
Resistors in Series
R1=1W
e0
R2=10W
Calculate the voltage across each resistor if
the battery has potential V0= 22 volts.
Simplify (R1 and R2 in series):
•R12 = R1 + R2
•V12 = V1 + V2
•I12 = I1 = I2
= 11 W
= V0 = 22 Volts
= V12/R12 = 2 Amps
e0
R12
Expand:
•V1 = I1R1
•V2 = I2R2
= 2 x 1 = 2 Volts
= 2 x 10 = 20 Volts
Check: V1 + V2 = V12 ?
Physics 102: Lecture 5, Slide 15
YES!
R1=1W
e0
R2=10W
Resistors in Parallel
• Two wires:
– Effectively adding the Area
– Since R a 1/A add 1/R:
1/Req = 1/R1 + 1/R2
R
Physics 102: Lecture 5, Slide 16
R
=
R/2
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
1 = Ieq = I1 + I2 = 1 + 1_
R1
Req
Veq
Veq
R1
R2
Physics 102: Lecture 5, Slide 17
R2
Req
Preflight 5.5
What happens to the current through R2 when the switch is
closed?
•
Increases
•
Remains Same
•
Decreases
ACT: Parallel Circuit
What happens to the current through the battery?
(1) Increases
(2) Remains Same
(3) Decreases
Physics 102: Lecture 5, Slide 18
Preflight 5.5
What happens to the current through R2 when the switch is
closed?
•
Increases
•
Remains Same
•
Decreases
V2 = ε = I2R2
ACT: Parallel Circuit
What happens to the current through the battery?
(1) Increases
(2) Remains Same
Ibattery = I2 + I3
(3) Decreases
Physics 102: Lecture 5, Slide 19
Practice:
Resistors in Parallel
e
R2
R3
Determine the current through the battery.
Let E = 60 Volts, R2 = 20 W and R3=30 W.
Simplify: R2 and R3 are in parallel
1/R23 = 1/R2 + 1/R3
V23 = V2 = V3
I23 = I2 + I3
Physics 102: Lecture 5, Slide 20
e
R23
Practice:
Resistors in Parallel
e
R2
R3
Determine the current through the battery.
Let E = 60 Volts, R2 = 20 W and R3=30 W.
Simplify: R2 and R3 are in parallel
1/R23 = 1/R2 + 1/R3 R23 = 12 W
V23 = V2 = V3 = 60 Volts
I23 = I2 + I3
Physics 102: Lecture 5, Slide 21
e
= V23 /R23 = 5 Amps
R23
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.
25 A
10 A
Toaster
5A
Coffee Pot
10 A
Microwave
This is dangerous because…
(By the way, power strips are wired in parallel.)
1. The resistance of the kitchen circuit is too high.
2. The voltage across the kitchen circuit is too high.
3. The current in the kitchen circuit is too high.
Physics 102: Lecture 5, Slide 22
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.
25 A
10 A
Toaster
5A
Coffee Pot
10 A
Microwave
This is dangerous because…
(By the way, power strips are wired in parallel.)
1. The resistance of the kitchen circuit is too high.
2. The voltage across the kitchen circuit is too high.
3. The current in the kitchen circuit is too high.
Physics 102: Lecture 5, Slide 23
Summary
Series
Parallel
R1
R1
R2
R2
Wiring
Each resistor on the
same wire.
Each resistor on a
different wire.
Voltage
Different for each resistor.
Vtotal = V1 + V2
Same for each resistor.
Vtotal = V1 = V2
Current
Same for each resistor
Itotal = I1 = I2
Different for each resistor
Itotal = I1 + I2
Increases
Req = R1 + R2
Decreases
1/Req = 1/R1 + 1/R2
Resistance
Physics 102: Lecture 5, Slide 24
Preflight 5.6, 5.7
1
Which configuration has the smallest resistance?
1
2
3
Which configuration has the largest resistance?
Physics 102: Lecture 5, Slide 25
2
3
Preflight 5.6, 5.7
1
R
2
2R
Which configuration has the smallest resistance?
1
2
3
Which configuration has the largest resistance?
2
Physics 102: Lecture 5, Slide 26
3
R/2
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!!
Physics 102: Lecture 5, Slide 27
See you next lecture!
• Read 18.5, 7
Physics 102: Lecture 5, Slide 28