Conductivity in solids
An electric current is a movement, or flow, of electric charge. Materials through which charge flows easily are called conductors, and those through which it does not flow easily are called insulators. There are some materials through which it flows with some difficulty, and these are called semi-conductors.
In the "old" days, before we knew about electrons, it was thought that electric charges flowed from what we call positive to what we call negative. With the discovery of electrons, it turned out that it is the "negative" electrons that move, and they move from negative places to positive places--so the electron current flows from - to + .
We make wires out of conductors, and wrap them with insulators so the charge does not leak out.
1. Which way does the electron current flow?
Conditions necessary for an electric current
Electric current through wires is in many ways very similar to water current through pipes. Why does water flow through a pipe? One way of looking at it is in terms of water pressure: water always flows from places of high pressure to places of low pressure. Electric potential is electrical "pressure", excepts it's a little backwards: electrons flow from places of low electric potential to places of high potential, if they are connected by a conducting pathway. A place where there are many electrons is a place of low potential. A place where many electrons are missing is a place of high potential.
Electric potential is measured in volts (V). Usually we are most concerned with the difference in potential between two places--the greater the electric potential difference, the more the electrons want to flow from the one place to the other. A voltmeter is a device used to measure the electric potential difference between two places. You just put the two probes of the voltmeter on the two places.
In the picture to the right we see a sequence of events. First there is a concentration of - charge, at low potential. When connected by a wire to the other, neutral sphere, current flows--but only for a while. When the charge on the right is just as concentrated as the charge on the left, the potentials are equal, and current no longer flows.
To get constant current to flow continously for long periods, we need a water pump--actually, an electron pump. One kind of electron pump is a wet or dry cell, commonly called a battery. Chemical energy ionizes molecules and provides a constant source of electrons (negative charge) on one end, and positive charge on the other, for a long time, at a constant potential difference, usually of about 1.5 volts .
To get a steady electric current to flow, then, you need a potential difference maintained between two places, and a conductor between them. If the whole path is isolated, or closed, it is called an electric circuit.
1. What conditions are needed for electric current to flow from one place to another?
2. What conditions are needed for an electric current to flow continuously (in a circuit)?
3. What does a voltmeter measure?
4. What are the units of electric potential difference?
Unit of electric current
The symbol for electric charge is q.
examples of use: q = -6.4 x 10-19 C, q = +3 C
Note: when we talk about charges that contain a very large number of elementary charges, such as +3 coulombs, we don't worry that 3 is not exactly divisible by 1.6 x 10-19. Any instrument we actually use to measure such charges is not nearly sensitive enough to detect a single elementary charge anyway.
The symbol for electric current is I, and the units are called amperes, or amps for short. The symbol for amp is A.
Electric current is composed of charges in motion. The more charges passing through a wire in a given time, the greater the current is. The equation is "current equals charge per time,"
The units of charge per time would be coulombs per second, so we see that one amp equals one coulomb per second (1A=1C/s).
1. If 10 coulombs of charge passes a given point in a conductor every 2 seconds, what is the current at that point?
2. A wire carries a current of 6.0 amperes. How much charge passes a point in the wire in 120 seconds?
The device used to measure electric current is called an ammeter. This is its symbol:
3. In the circuit shown to the right, how many coulombs of charge will pass through resistor R in 2.0 seconds?
4. How much charge passes through a wire carrying 2.0 microamps in a time of
3.0 seconds?
5. How long does it take for 20 C of charge to pass through a resistor carrying a current of 4 A ?
OHM’S LAW
An ohmic conductor is one which obeys Ohm’s Law: the current flowing through the resistor is directly proportional to the potential difference applied.
Since R= by definition, this means that an ohmic conductor has a constant resistance, unaffected by V. Even if you vary V, the ratio remains constant. By contrast, a non-ohmic conductor, such as a semiconductor, has different R depending on the V.
Conductors obey Ohm's Law. Insulators and semi-conductors do not obey Ohm's Law. For example, if the potential difference between a cloud and the earth is 5000V there may be no current flow at all, but if it gets up to 50,000 V there may be a huge current, (lightning, of course!) The current that flows through air is not directly proportional to the potential difference applied.
The equation is usually itself called “Ohm’s Law”. This makes sense as long as we are talking about a conductor. Commercially available resistors obey Ohm’s Law, and they are labeled (color-coded) with their resistance, which is the same for small voltages or large voltages.
We can also write the equation as V=IR (electricians write it this way). If we write it like this: it shows more clearly that the current, I, that flows through the part of the circuit containing the resistor depends on two things: V, and R. Increasing V increases the current. Increasing R decreases the current.
Questions:
1. A 12 volt battery is connected to a 3 ohm resistor. How much current flows?
2. What potential difference is needed to get a 2 amp current to flow through a circuit containing a 20 ohm resistance?
3. A 50 amp current flows through a wire. The resistance is doubled…what is the new current?
4. Which obeys Ohm’s Law?
Resistance of a conductor (factors affecting R)
Conductors have low resistance to the flow of electric current; insulators have high resistance. The symbol for resistance is R, and its units are called ohms (symbol ).
Four main factors affect the resistance of a solid conducting object, such as a copper wire:
1) Obviously, the substance it is made of.
2) The length; R is directly proportional to the object's length.
3) The cross-sectional area of the wire; the greater the cross-sectional area, the lower the resistance (inversely proportional). Think of it this way--the wire is a path for electrons, and the wider the path, the easier it is for electrons to travel on it.
4) The temperature--the higher the temperature, the higher the resistance (directly proportional). Reason: heating it makes the atoms vibrate faster, and the electrons are more likely to collide into atoms as they travel through the wire.
An object's resistance is defined as the ratio of the potential difference between the two ends and the current flowing through it: R=V/I . If a small V makes a lot of current (I) flow, the object has a low resistance. Large V, but small I, means high resistance.
1. What is the symbol for resistance? Its units? The units' symbol?______
2. A wire has a resistance of R. For each change, state what the new resistance is.
ex: Length is doubled. ans: 2R
a. Length is tripled.______
b. Length is halved.______
c. Cross-sectional area doubled.______
d. Cross-sectional area tripled.______
e. Length doubled and cross-sectional area doubled.______
f. Length doubled and cross-sectional area halved.______
g. Length tripled and cross-sectional area halved.______
3. What is the resistance of a wire through which 20A flows when 40V is applied to the two ends?______
4. A copper wire's resistance is 4. How much current flows when a potential difference of 20V is applied?______
5. What potential difference is needed to make 6 amps flow through a 2 ohm resistor?
______
Resistivity, , is a measure of how poorly a conductor is the substance a wire is made of . For a wire of length L and cross-sectional areaA, .
Use the chart in the Reference Tables, “Resistivities at 20o C,” to get the values.
6. Calculate the resistance of a 1.2 meter copper wire with a cross-sectional area of 1.0 x 10-5 m2.
7. Calculate the resistance of a 30.0 meter silver wire with a radius of .03 m.
Electrical quantities and their Units
You need to know all the symbols, for quantities and for units, and what they stand for, and be able to match up quantities and their units. If not, you’ll be hopelessly lost, utterly confused, and in general have a tough time solving problems.
Some of this information is in the Reference Tables, and some needs to be memorized, and memorized well, so that you’re not guessing when you need to use it.
Quantity / Symbol for the quantity / Units / Symbol for the units / Equivalent unitscharge / q / coulombs / C / 1 C = 6.25 x 1018 e
charge / q / elementary charge / e / 1 e = 1.60 x 10-19 C
current / I / amps / A / C/s
potential difference / V / volts / V / J/C
resistance / R / ohms / / V/A
resistivity / / ohm·meters / ·m / ------
work, energy / W / joule / J / 1 J = 6.25 x 1018 eV
work, energy / W / electron-volt / eV / 1 eV = 1.60 x 10-19 J
power / P / watts / W / J/s
Memorize Mr. Hees’s poem!
Meters
Ammeters measure current at a point in the circuit, and are connected in series with a device. They have low resistance so as not to significantly reduce the current that had been flowing before the meter was added.
Voltmeters measure potential difference between two locations, or “across a resistor.” They are connected in parallel with a device, and have high resistance.
1. What kind of meter measures potential difference?______
2. What kind of meter measures current?______
!!3. What kind of meter measures resistance?______
4. ______-meters have low resistance because we want virtually all the current to pass through them as they measure ______through a device. ______-meters have high resistance, so that virtually ______current passes through them.
Series Circuits
Two or more resistors can be wired together in two different ways: in series, or in parallel.
In a series circuit, electric current flows through all the resistors, one after another. One path.
1. Draw a circuit diagram of a circuit with a cell and 2 resistors in series, R1 and R2.
2. Draw a circuit with a cell and 3 resistors in series.
The current flowing through R1 is the same as that flowing through R2, etc.
IT = I1 = I2 = I3 = …
3. Three resistors (1, 2, and 3) are connected in series. If 2 amps flows through the 1 resistor, how much current flows through the 3 resistor?
The total, or equivalent resistance is the sum of all the individual resistances.
Req = R1 + R2 + R3 + ... (Sometimes we write RTotal or RT instead of Req)
4. What is the equivalent resistance of a circuit containing these three resistors, connected in series? 1, 2, and 3
To measure the current passing through a particular resistor, an ammeter is placed in series with it.
5. Draw a circuit with a single resistor and an ammeter measuring the current through it.
6. A series circuit contains five 6-ohm resistors. A 120 volt power source is connected to it. How much current flows through the circuit?
7. What potential difference is needed to cause 7 amps to flow through a circuit containing a 4.5, a 2, and a 3 resistor all wired in series?
The difference between the electric potential at one side of a resistor and at the other side of the same resistor is often called the voltage drop. It’s like a step down. The total voltage of the circuit equals the sum of the individual voltage drops.
VT = V1 + V2 + V3 + …
8. Two devices are in series with a 6 volt battery. The voltage drop across one of the devices is 5.3 V. What is the voltage drop across the other one?
Parallel Circuits
Two or more resistors can be wired together in two different ways: in series, or in parallel.
In a parallel circuit, electric current splits up at a junction. Some of the current flows through the first resistor, some through the second, and so on. All the current meets again at the junction where the resistors join together. IT = I1 + I2 + I3 + …
1. The total current pushed by a voltage source is 12 A. Two devices are connected in parallel. Three amps pass through the first. How much current passes through the second device?
2. Draw a circuit diagram of a circuit with a cell and 2 resistors in parallel, R1 and R2.
3. Draw a circuit with 3 resistors in parallel with a cell.
The potential difference across R1 is the same as that across R2, etc.
4. Three resistors (1, 2, and 3) are connected in parallel. If the potential difference across the 1 resistor is 3 volts, what is the potential difference across the 3 resistor?
The reciprocal of the total (equivalent) resistance is thesum of the reciprocals of all the individual resistances.
5. What is the equivalent resistance of a circuit containing two 4 resistors, connected in parallel?
6. What is the equivalent resistance of a circuit containing a1 resistor and a 2 resistor, connected in parallel?
7. What is the equivalent resistance of a circuit containing these three resistors, connected in parallel? 1, 2, and 3
To measure the potential difference across a particular resistor, a voltmeter is placed in parallel with it.
8. Draw a circuit with a single resistor and a voltmeter measuring the potential difference across it.
Each device wired in parallel gets the full, total voltage. Even though the current splits up among the different paths, the voltage doesn’t.
VT = V1= V2= V3= …
9. A parallel circuit contains five 6-ohm resistors. A 120 volt power source is connected to it. What is the voltage across each resistor? ______How much total current flows through the circuit?
Power & energy in electric circuits
Remember: Power = energy/time (joules per second).
It takes energy to make electrons go through a circuit. Where does the energy go? Any part of the circuit that offers resistance heats up as the electrons travel through it. We say the thing "dissipates" energy in the form of heat.
We can express the power that a part of the circuit dissipates in terms of any two of the three quantities V, I, and R:
P = VI and P = I2R andalso P = V2/R
Since they are all equal, we can condense them into one equation: P = VI = I2R = V2/R .
1. How much power is dissipated by a 5 resistor which carries 2 amps?
2. How much power is dissipated in a circuit connected to a 9 volt battery, which pushes 0.1 amps?
3. How many joules per second are used by a 4 resistor hooked up to a 3 volt battery?
The total energy dissipated by a resistor is just the power multiplied by the time it is in operation (joules per second times seconds equals joules). We will use the symbol W to stand for energy (it is the work done to move the electrons through the circuit).
W=Pt
4. How much power is used by a computer if it uses 200 joules in 10 seconds?
5. How much time is needed for 20 joules to be used by a 16 W motor?
6. How much energy is used by a 1000-watt hair dryer in 40 seconds?
7. How much energy is used in 60 seconds by a toaster oven plugged into a 120-volt outlet, if 3 amps flows through it?
8. How much energy is used in 2 minutes if 2 amps flows through a 3 resistor?