1-30-98
Relevant sections in the textbook : 20.2 - 20.5
A battery produces direct current; the battery voltage (or emf) is constant, which generally results in a constant current flowing one way around a circuit. If the circuit has capacitors, which store charge, the current may not be constant, but it will still flow in one direction. The current that comes from a wall socket, on the other hand, is alternating current. With alternating current, the current continually changes direction. This is because the voltage (emf) is following a sine wave oscillation, changing from positive to negative and back again 60 times each second.
If you look at the voltage at its peak, it hits about +170 V, decreases through 0 to -170 V, and then rises back through 0 to +170 V again. (You might think this value of 170 V should really be 110 - 120 volts. That's actually a kind of average of the voltage, but the peak really is about 170 V.) This oscillating voltage produces an oscillating electric field; the electrons respond to this oscillating field and oscillate back and forth, producing an oscillating current in the circuit.
Voltage can be thought of as the pressure pushing charges along a conductor, while the electrical resistance of a conductor is a measure of how difficult it is to push the charges along. Using the flow analogy, electrical resistance is similar to friction. For water flowing through a pipe, a long narrow pipe provides more resistance to the flow than does a short fat pipe. The same applies for flowing currents: long thin wires provide more resistance than do short thick wires.
The resistance (R) of a material depends on its length, cross-sectional area, and the resistivity (r ), a number that depends on the material:
The resistivity and conductivity are inversely related. Good conductors have low resistivity, while poor conductors (insulators) have resistivities that can be 20 orders of magnitude larger.
Resistance also depends on temperature, usually increasing as the temperature increases. For reasonably small changes in temperature, the change in resistivity, and therefore the change in resistance, is proportional to the temperature change. This is reflected in the equations:
At low temperatures some materials, known as superconductors, have no resistance at all. Resistance in wires produces a loss of energy (usually in the form of heat), so materials with no resistance produce no energy loss when currents pass through them.
In many materials, the voltage and resistance are connected by Ohm's Law:
Ohm's Law : V = IR
The connection between voltage and resistance can be more complicated in some materials.These materials are called non-ohmic. We'll focus mainly on ohmic materials for now, those obeying Ohm's Law.
A copper wire has a length of 160 m and a diameter of 1.00 mm. If the wire is connected to a 1.5-volt battery, how much current flows through the wire?
The current can be found from Ohm's Law, V = IR. The V is the battery voltage, so if R can be determined then the current can be calculated. The first step, then, is to find the resistance of the wire:
L is the length, 1.60 m. The resistivity can be found from the table on page 591 in the textbook.
The area is the cross-sectional area of the wire. This can be calculated using:
The resistance of the wire is then:
The current can now be found from Ohm's Law:
I = V / R = 1.5 / 3.5 = 0.428 A
Power is the rate at which work is done. It has units of Watts. 1 W = 1 J/s
Electric power is given by the equations:
The power supplied to a circuit by a battery is calculated using P = VI.
Batteries and power supplies supply power to a circuit, and this power is used up by motors as well as by anything that has resistance. The power dissipated in a resistor goes into heating the resistor; this is know as Joule heating. In many cases, Joule heating is wasted energy. In some cases, however, Joule heating is exploited as a source of heat, such as in a toaster or an electric heater.
The electric company bills not for power but for energy, using units of kilowatt-hours.
One kW-h typically costs about 10 cents, which is really quite cheap. It does add up, though. The following equation gives the total cost of operating something electrical:
Cost = (Power rating in kW) x (number of hours it's running) x (cost per kW-h)
An example...if a 100 W light bulb is on for two hours each day, and energy costs $0.10 per kW-h, how much does it cost to run the bulb for a month?
Cost = 0.1 kW x 60 hours x $0.1/kW-h = $0.6, or 60 cents.
Try this at home - figure out the monthly cost of using a particular appliance you use every day. Possibilities include hair dryers, microwaves, TV's, etc. The power rating of an appliance like a TV is usually written on the back, and if it doesn't give the power it should give the current. Anything you plug into a wall socket runs at 120 V, so if you know that and the current you can figure out how much power it uses.
The cost for power that comes from a wall socket is relatively cheap. On the other hand, the cost of battery power is much higher. $100 per kW-h, a thousand times more than what it costs for AC power from the wall socket, is a typical value.
Although power is cheap, it is not limitless. Electricity use continues to increase, so it is important to use energy more efficiently to offset consumption. Appliances that use energy most efficiently sometimes cost more but in the long run, when the energy savings are accounted for, they can end up being the cheaper alternative.