Download PES 1120 Spring 2014, Spendier Lecture 21/Page 1 Today

PES 1120 Spring 2014, Spendier
Lecture 21/Page 1
Today:
- Power
- Superconductors
Last time we stopped at Ohm’s law:
V = IR
- V…potential difference [V] Volts
- I … rate at which charges move = dq/dt [A] Ampere
- R… Resistance to current moving = ρL/A  
Today, we will talk about electrical power:
What Is Electrical Power?
Consider a device that has a voltage across it and a current flowing
through it. That situation is shown in the diagram at the left.
The voltage across the device is a measure of the energy - in joules - that
a unit charge - one coulomb - will dissipate when it flows through the
device.
If the device is a resistor, then the energy will appear as heat energy in
the resistor. If the device is a battery, then the energy will be stored in
the battery.
The current is the number of coulombs that flows through the device in
one second.
If each coulomb dissipates V joules, and I coulombs flows in one second, then the rate of
energy dissipation is the product, VI.
Power: P = IV [J/s] energy per time of [W] Watt
That's what power is - the rate at which energy is expended. It doesn't matter what
the electrical device is, the rate at which energy is delivered to the device is VI
Book derivation:
Charge dq moves through a decrease in potential of magnitude V, and thus its electric
potential energy decreases in magnitude by the amount
dU = dq V
dU dq
 V
dt
dt
Power: P = IV [J/s] energy per time of [W] Watt
PES 1120 Spring 2014, Spendier
Lecture 21/Page 2
This power P is the rate at which energy is transferred from the battery to the unspecified
device.
1) If that device is a motor connected to a mechanical load, the energy is transferred
as work done on the load.
2) If the device is a storage battery that is being charged, the energy is transferred to
stored chemical energy in the storage battery.
3) If the device is a resistor, the energy is transferred to internal thermal energy,
tending to increase the resistor’s temperature.
Let’s focus on 3)
As an electron moves through a resistor at constant drift speed, its average kinetic energy
remains constant and its lost electric potential energy appears as thermal energy in the
resistor and the surroundings. On a microscopic scale this energy transfer is due to
collisions between the electron and the molecules of the resistor, which leads to an
increase in the temperature of the resistor lattice. The mechanical energy thus transferred
to thermal energy is dissipated (lost) because the transfer cannot be reversed.
NOTE ONLY For a resistor or some other device with resistance R, we can combine
P = IV
With
V = IR
To get: P  I 2 R 
V2
R
Caution: We must be careful to distinguish
P = IV
That applies to electrical energy transfers of all kinds;
And
V2
PI R
R
That apply only to the transfer of electric potential energy to thermal energy in a device
with resistance.
2
PES 1120 Spring 2014, Spendier
Lecture 21/Page 3
Example 1:
The average bulk resistivity of the human body (apart from surface resistance of the skin)
is about 5   m The conducting path between the hands can be represented
approximately as a cylinder 1.25 m long and 0.2 m in diameter. The skin resistance can
be made negligible by soaking the hands in salt water.
a) What is the resistance between the hands if the skin resistance is made negligible?
b) What potential difference between the hands is needed for a lethal shock current of
100mA? (Note that your results shows that small potential differences produce dangerous
currents when the skin is damp.)
c) With the current in part (b), what power is dissipated in the body? Is it enough power
to run a light bulb?
Light bulb: 30-60 W.
PES 1120 Spring 2014, Spendier
Lecture 21/Page 4
Example 2: A 1250 W radiant heater is constructed to operate at 115 V.
a) What is the current in the heater when the unit is operating?
b) What is the resistance of the heating coil?
c) How much thermal energy is produced in 1.0 h?
Typically we ignore resistance of wires in a circuit since it this negligible compared to
that of the resistor. However, when transferring electricity over long distances through
power lines, the resistance of the wires is no longer negligible.
Example 3: A small power plant produces a voltage of 6.0 kV and 150 A. The resistance
of the transmission line between the power plants and the substation is 75 Ohms.
What is the power loss?
P = I2 R = (150)2(75) = 1.7 MW
This is a lot!
How can we reduce this? We can reduce this by lowering the current and stepping
voltage up, like a "transformer" does.
OR we can reduce resistance - superconductors!
PES 1120 Spring 2014, Spendier
Lecture 21/Page 5
Superconductors
Superconductors, materials that have no resistance to the flow of electricity, are one of
the last great frontiers of scientific discovery. Not only have the limits of
superconductivity not yet been reached, but the theories that explain superconductor
behavior seem to be constantly under review. In 1911 superconductivity was first
observed in mercury by Dutch physicist Heike Kamerlingh Onnes. When he cooled it to
the temperature of liquid helium, 4 degrees Kelvin (-452F, -269C), its resistance
suddenly disappeared. The Kelvin scale represents an "absolute" scale of temperature.
Thus, it was necessary for Onnes to come within 4 degrees of the coldest temperature that
is theoretically attainable to witness the phenomenon of superconductivity. Later, in
1913, he won a Nobel Prize in physics for his research in this area.
Significance of this discovery: No resistance:
- current can flow without a voltage!
V = IR
I = V/R
- In a superconducting material making a loop, once current starts it won't stop.
- We have zero energy loss: P = 0
It costs a lot of $ to cool things down - today we have found other superconducting
materials at higher temperatures:
PES 1120 Spring 2014, Spendier
Lecture 21/Page 6
The current record critical temperature is about Tc = 133 K (−140 °C) at standard
pressure, and somewhat higher critical temperatures can be achieved at high pressure.
Nevertheless at present it is considered unlikely that copper-oxide materials will achieve
room-temperature superconductivity.
Uses of superconductors
Superconductors are used in the following applications:
- Maglev (magnetic levitation) trains. These work because a superconductor repels a
magnetic field so a magnet will float above a superconductor – this virtually eliminates
the friction between the train and the track. However, there are safety concerns about the
strong magnetic fields used as these could be a risk to human health.
- Large hadron collider or particle accelerator Superconductors are used to make
extremely powerful electromagnets to accelerate charged particles very fast (to near the
speed of light).
- SQUIDs (Superconducting QUantum Interference Devices) are used to detect even the
weakest magnetic field. They are used in mine detection equipment to help in the
removal of land mines. We have a SQUID here at UCCS
- The USA is developing “E-bombs”. These are devices that make use of strong,
superconductorderived magnetic fields to create a fast, high-intensity electromagnetic
pulse that can disable an enemy’s electronic equipment. These devices were first used in
wartime in March 2003 when USA forces attacked an Iraqi broadcast facility. They can
release two billion watts of energy at once.
The following uses of superconductors are under development:
- Making electricity generation more efficient
- Very fast computing. (supercomputers)
Other impacts of superconductors on technology will depend on either finding
superconductors that work at far higher temperatures than those known at present, or
finding cheaper ways of achieving the very cold temperatures currently needed to make
them work.