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Ch. 21: Electric circuits, currents, Ohm’s Law, electric power - +

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Ch. 21: Electric circuits, currents, Ohm’s Law, electric power - +
Ch. 21: Electric circuits, currents, Ohm’s
Law, electric power
(Dr. Andrei Galiautdinov, UGA)
2014FALL - PHYS1112
+
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Al
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PLAN:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
The need for steady current I; definition of I = ΔQ/ Δt
Capacitor can maintain current for only a brief period of time
Transforming a capacitor into a battery: the need for a “workhorse”
inside to maintain charge separation on (and potential difference
between) battery’s terminals
Making our own battery
Our own battery is not ideal: if we drain too much current (even at I =
1 [mA]), the “workhorse” can’t keep up with the demand; the Vb drops
significantly
Ideal batteries maintain Vb no matter how much I is drawn; from now
on all our batteries will be ideal
Power dissipated in a circuit element: P = I V
Ohm’s Law: I = V/R
Simple circuits contain only one battery
Resistors in series: R = R1 + R2 + R3 + …
Resistors in parallel: 1/R = 1/R1 + 1/R2 + 1/R3 + …
Examples: simple cases
Example: overloading the circuit
1
In order to have a steady current, we need to
maintain a steady potential difference:
A charged capacitor can maintain a (decreasing) potential
difference for only a brief period of time, so it’s not a good
source of current! We need something more stable.
2
Pretty much the same as before; just
showing in detail how the light bulb
really looks like on the inside.
3
André-Marie Ampère (20 January 1775 – 10
June 1836), professor of mathematics at the
Ecole Polytechnique, a short time after learning
of Ørsted's discovery that magnetic needle is
acted on by a voltaic current, conducts
experiments and publishes a paper in Annales
de Chimie et de Physique (1820) attempting to
give a combined theory of electricity and
magnetism.
He shows that a coil of wire carrying a current
behaves like an ordinary magnet and suggests
that electromagnetism might be used in
telegraphy. He mathematically develops
Ampère's law describing the magnetic force
between two electric currents. His theory
predicts that parallel conductors currying
current in the same direction attract and those
carrying currents in the opposite directions
repel one another.
One of the first to develop electrical measuring
techniques, he built an instrument utilizing a
free-moving needle to measure the flow of
electricity, contributing to the development of
the galvanometer, and, later, ammeter.
The SI unit of measurement of electric current,
4
the ampere, is named after him.
PLAN:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
The need for steady current I; definition of I = ΔQ/ Δt
Capacitor can maintain current for only a brief period of time
Transforming a capacitor into a battery: the need for a “workhorse”
inside to maintain charge separation on (and potential difference
between) battery’s terminals
Making our own battery
Our own battery is not ideal: if we drain too much current (even at I =
1 [mA]), the “workhorse” can’t keep up with the demand; the Vb drops
significantly
Ideal batteries maintain Vb no matter how much I is drawn; from now
on all our batteries will be ideal
Power dissipated in a circuit element: P = I V
Ohm’s Law: I = V/R
Simple circuits contain only one battery
Resistors in series: R = R1 + R2 + R3 + …
Resistors in parallel: 1/R = 1/R1 + 1/R2 + 1/R3 + …
Examples: simple cases
Example: overloading the circuit
5
Our own battery:
b
Something inside the battery has to
push charges against electrostatic
force. We need a workhorse. The
energy for such “pushing” comes
from the workhorse (typically, from
chemical reactions).
6
PLAN:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
The need for steady current I; definition of I = ΔQ/ Δt
Capacitor can maintain current for only a brief period of time
Transforming a capacitor into a battery: the need for a “workhorse”
inside to maintain charge separation on (and potential difference
between) battery’s terminals
Making our own battery
Our own battery is not ideal: if we drain too much current (even at I =
1 [mA]), the “workhorse” can’t keep up with the demand; the Vb drops
significantly
Ideal batteries maintain Vb no matter how much I is drawn; from now
on all our batteries will be ideal
Power dissipated in a circuit element: P = I V
Ohm’s Law: I = V/R
Simple circuits contain only one battery
Resistors in series: R = R1 + R2 + R3 + …
Resistors in parallel: 1/R = 1/R1 + 1/R2 + 1/R3 + …
Examples: simple cases
Example: overloading the circuit
7
PLAN:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
The need for steady current I; definition of I = ΔQ/ Δt
Capacitor can maintain current for only a brief period of time
Transforming a capacitor into a battery: the need for a “workhorse”
inside to maintain charge separation on (and potential difference
between) battery’s terminals
Making our own battery
Our own battery is not ideal: if we drain too much current (even at I =
1 [mA]), the “workhorse” can’t keep up with the demand; the Vb drops
significantly
Ideal batteries maintain Vb no matter how much I is drawn; from now
on all our batteries will be ideal
Power dissipated in a circuit element: P = I V
Ohm’s Law: I = V/R
Simple circuits contain only one battery
Resistors in series: R = R1 + R2 + R3 + …
Resistors in parallel: 1/R = 1/R1 + 1/R2 + 1/R3 + …
Examples: simple cases
Example: overloading the circuit
8
PLAN:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
The need for steady current I; definition of I = ΔQ/ Δt
Capacitor can maintain current for only a brief period of time
Transforming a capacitor into a battery: the need for a “workhorse”
inside to maintain charge separation on (and potential difference
between) battery’s terminals
Making our own battery
Our own battery is not ideal: if we drain too much current (even at I =
1 [mA]), the “workhorse” can’t keep up with the demand; the Vb drops
significantly
Ideal batteries maintain Vb no matter how much I is drawn; from now
on all our batteries will be ideal
Power dissipated in a circuit element: P = I V
Ohm’s Law: I = V/R
Simple circuits contain only one battery
Resistors in series: R = R1 + R2 + R3 + …
Resistors in parallel: 1/R = 1/R1 + 1/R2 + 1/R3 + …
Examples: simple cases
Example: overloading the circuit
9
In this simplest example, a single circuit element (light bulb) is DIRECTLY
connected to the battery.
10
Similar situation, different values.
11
Work done by the electric
field while pushing charges
across a circuit element is
dissipated in the form of
heat and, possibly, light.
12
PLAN:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
The need for steady current I; definition of I = ΔQ/ Δt
Capacitor can maintain current for only a brief period of time
Transforming a capacitor into a battery: the need for a “workhorse”
inside to maintain charge separation on (and potential difference
between) battery’s terminals
Making our own battery
Our own battery is not ideal: if we drain too much current (even at I =
1 [mA]), the “workhorse” can’t keep up with the demand; the Vb drops
significantly
Ideal batteries maintain Vb no matter how much I is drawn; from now
on all our batteries will be ideal
Power dissipated in a circuit element: P = I V
Ohm’s Law: I = V/R
Simple circuits contain only one battery
Resistors in series: R = R1 + R2 + R3 + …
Resistors in parallel: 1/R = 1/R1 + 1/R2 + 1/R3 + …
Examples: simple cases
Example: overloading the circuit
13
Georg Simon Ohm (16 March 1789 – 6 July
1854) was a German physicist and
mathematician.
As a high school teacher, Ohm began his
research with the new electrochemical cell,
invented by Italian scientist Alessandro
Volta.
Using equipment of his own creation, Ohm
found that there is a direct proportionality
between the potential difference (voltage)
applied across a conductor and the
resultant electric current.
This relationship is known as Ohm's law:
I = V/R
14
15
16
PLAN:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
The need for steady current I; definition of I = ΔQ/ Δt
Capacitor can maintain current for only a brief period of time
Transforming a capacitor into a battery: the need for a “workhorse”
inside to maintain charge separation on (and potential difference
between) battery’s terminals
Making our own battery
Our own battery is not ideal: if we drain too much current (even at I =
1 [mA]), the “workhorse” can’t keep up with the demand; the Vb drops
significantly
Ideal batteries maintain Vb no matter how much I is drawn; from now
on all our batteries will be ideal
Power dissipated in a circuit element: P = I V
Ohm’s Law: I = V/R
Simple circuits contain only one battery
Resistors in series: R = R1 + R2 + R3 + …
Resistors in parallel: 1/R = 1/R1 + 1/R2 + 1/R3 + …
Examples: simple cases
Example: overloading the circuit
17
18
19
20
PLAN:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
The need for steady current I; definition of I = ΔQ/ Δt
Capacitor can maintain current for only a brief period of time
Transforming a capacitor into a battery: the need for a “workhorse”
inside to maintain charge separation on (and potential difference
between) battery’s terminals
Making our own battery
Our own battery is not ideal: if we drain too much current (even at I =
1 [mA]), the “workhorse” can’t keep up with the demand; the Vb drops
significantly
Ideal batteries maintain Vb no matter how much I is drawn; from now
on all our batteries will be ideal
Power dissipated in a circuit element: P = I V
Ohm’s Law: I = V/R
Simple circuits contain only one battery
Resistors in series: R = R1 + R2 + R3 + …
Resistors in parallel: 1/R = 1/R1 + 1/R2 + 1/R3 + …
Examples: simple cases
Example: overloading the circuit
21
We want to know how much power is dissipated in the wiring of a dormitory, as heaters are being
added up. The wiring is modeled by a single resistor r.
22
First heater is turned on.
Rwire
central switch
23
Second heater is turned on.
Rwire
central switch
24
Kirchhoff’s Rules
25
26
Practice problems
27
Problem 1.
1) A car battery does 260 J of work on the charge
passing through it as it starts an engine. If the emf
of the battery is 12V, how much charge passes
through the battery during the start?
28
29
Problem 1.
1) A car battery does 260 J of work on the charge
passing through it as it starts an engine. If the emf
of the battery is 12V, how much charge passes
through the battery during the start?
22 C
30
Problem 2.
2) A television set connected to a 120-V outlet
consumes 85 W of power. (a) How much current
flows through the television? (b) How long does it
take for 10 million electrons to pass through the
TV?
31
32
Problem 2.
2) A television set connected to a 120-V outlet
consumes 85 W of power. (a) How much current
flows through the television? (b) How long does it
take for 10 million electrons to pass through the
TV?
(a) 0.71 A; (b) 2 x 10-12 s
33
Problem 3.
3) Pacemakers designed for long-term use
commonly employ a lithium-iodine battery capable
of supplying 0.42 A∙h of charge. (a) How many
coulombs of charge can such a battery supply?
(b) If the average current produced by the
pacemaker is 5.6 μA, what is the expected lifetime
of the device?
34
35
Problem 3.
3) Pacemakers designed for long-term use
commonly employ a lithium-iodine battery capable
of supplying 0.42 A∙h of charge. (a) How many
coulombs of charge can such a battery supply?
(b) If the average current produced by the
pacemaker is 5.6 μA, what is the expected lifetime
of the device?
(a) 1500 C; (b) 8.6 years
36
37
38
39
The End
40
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