Electric currents carry electrical energy that can be transformed into other forms of energy.
22.1 Current and Circuits
Main Idea
Electric current is the flow of electric charges.
Essential Questions
What is electric current?
How can you think about energy in electric circuits?
What is Ohm’s law?
How are power, current, potential difference, and resistance mathematically related?
Review Vocabulary
Electric potential difference: The work done moving a positive test charge between two points in an electric field divided by the magnitude of that test charge.
New Vocabulary
Electric current
Conventional current
Battery
Electric circuit
Ampere
Resistance
Resistor
Parallel connection
Series connection
Producing Electric Current
Flowing water at the top of a waterfall has both potential and kinetic energy.
The large amount of natural potential and kinetic energy available from resources such as Niagara Falls are of little use unless that energy can be transported efficiently.
Electric energy provides the means to transfer large quantities of energy over great distances with little loss.
This transfer is usually done at high potential differences through power lines.
Once this energy reaches the consumer, it can easily be converted into another form or combination of forms, including sound, light, thermal energy, and motion.
Because electric energy can so easily be changed into other forms, it has become indispensable in our daily lives.
When two conducting spheres touch, charges flow from the sphere at a higher potential to the one at a lower potential.
The flow continues until there is no potential difference between the two spheres.
A flow of charged particles is an electric current.
In a circuit with conductors A and B connected by a wire C, charges flow from the higher potential of B to A through C until the potential difference between A, B, and C is zero.
The direction in which a positive test charge moves is called conventional current.
Usually, it is the negative charges (electrons) that flow. The flow of electrons and the direction of the conventional current are in opposite directions.
The electric potential difference can be maintained by pumping charged particles from A back to B, which requires an external energy source.
A voltaic or galvanic cell (a common dry cell) converts chemical energy to electric energy.
A battery is made up of several galvanic cells connected together.
A photovoltaic cell, or solar cell, changes light energy into electric energy.
Electric Circuits
Charges move around a closed loop, cycling from a pump B, through C to A, and back to the pump.
Any closed loop or conducting path allowing electric charges to flow is called an electric circuit.
A circuit includes a charge pump, which increases the potential energy of the charges and a device that reduces the potential energy of the charges.
The potential energy lost by the charges, qV, moving through the device is usually converted into some other form of energy.
Electric energy is converted to kinetic energy by a motor, to light energy by a lamp, and to thermal energy by a heater.
A charge pump creates the flow of charged particles that make up a current.
Charges cannot be created or destroyed, but they can be separated.
The total amount of charge in the circuit does not change.
If one coulomb flows through the generator in 1 s, then one coulomb also will flow through the motor in 1 s.
Charge is a conserved quantity.
Energy is also conserved.
The change in electric energy, \Delta E, equals qV.
Because q is conserved, the net change in potential energy of the charges going completely around the circuit must be zero.
The increase in potential difference produced by the generator equals the decrease in potential difference across the motor.
Rates of Charge Flow and Energy Transfer
Power, which is defined in watts, W, measures the rate at which energy is transferred.
If a generator transfers 1 J of kinetic energy to electric energy each second, it is transferring energy at the rate of 1 J/s, or 1 W.
The energy carried by an electric current depends on the charge transferred, q, and the potential difference across which it moves, V. Thus, E = qV.
The unit for the quantity of electric charge is the coulomb.
The rate of flow of electric charge, q/t, called electric current, is measured in coulombs per second.
Electric current is represented by I, so I = q/t.
A flow of 1 C/s is called an ampere, A.
The energy carried by an electric current is related to the voltage, E = qV.
Since current, I = q/t, is the rate of charge flow, the power, P = E/t, of an electric device can be determined by multiplying voltage and current.
To derive the familiar form of the equation for the power delivered to an electric device, you can use P = E/t and substitute E = qV and q = It
P = IV
Power is equal to the current times the potential difference.
Diagramming Circuits
An electric circuit is drawn using standard symbols for the circuit elements.
Such a diagram is called a circuit schematic.
An ammeter measures current and a voltmeter measures potential differences.
Each instrument has two terminals, usually labeled + and –. A voltmeter measures the potential difference across any component of a circuit.
When connecting the voltmeter in a circuit, always connect the + terminal to the end of the circuit component that is closer to the positive terminal of the battery, and connect the – terminal to the other side of the component.
Resistance and Ohm’s Law
If two conductors have a potential difference between them, connecting them with a copper rod creates a large current, while using a glass rod creates almost no current.
The property determining how much current will flow is called resistance.
Resistance is measured by placing a potential difference across a conductor and dividing the voltage by the current.
The resistance, R, is defined as the ratio of electric potential difference, V, to the current, I.
Resistance is equal to voltage divided by current.
R = V/I
The resistance of the conductor, R, is measured in ohms.
One ohm (1 Ω) is the resistance permitting an electric charge of 1 A to flow when a potential difference of 1 V is applied across the resistance.
Georg Simon Ohm found that the ratio of potential difference to current is constant for a given conductor.
The resistance for most conductors does not vary as the magnitude or direction of the potential applied to it changes.
A device having constant resistance independent of the potential difference obeys Ohm’s law.
Most metallic conductors obey Ohm’s law, at least over a limited range of voltages.
Many important devices, such as transistors and diodes in radios and pocket calculators, and lightbulbs do not obey Ohm’s law.
Wires used to connect electric devices have low resistance.
A 1-m length of a typical wire used in physics labs has a resistance of about 0.03 Ω.
Because wires have so little resistance, there is almost no potential drop across them.
To produce greater potential drops, a large resistance concentrated into a small volume is necessary.
A resistor is a device designed to have a specific resistance.
Resistors may be made of graphite, semiconductors, or wires that are long and thin.
There are two ways to control the current in a circuit:
Varying V
Varying R
Because I = V/R, I can be changed by varying V, R, or both.
According to Ohm’s law, the greater the voltage placed across a resistor, the larger the current passing through it.
If the current through a resistor is cut in half, the potential difference also is cut in half.
Resistors often are used to control the current in circuits or parts of circuits.
Sometimes, a smooth, continuous variation of the current is desired.
For example, the speed control on some electric motors allows continuous, rather than step-by-step, changes in the rotation of the motor.
Some variable resistors consist of a coil of resistance wire and a sliding contact point.
Moving the contact point to various positions along the coil varies the amount of wire in the circuit.
As more wire is placed in the circuit, the resistance of the circuit increases; thus, the current changes in accordance with the equation I = V/R.
In this way, the speed of a motor can be adjusted from fast, with little wire in the circuit, to slow, with a lot of wire in the circuit.
Other examples of using variable resistors to adjust the levels of electrical energy can be found on the front of a TV: the volume, brightness, contrast, tone, and hue controls are all variable resistors.
The human body acts as a variable resistor.
When dry, skin’s resistance is high enough to keep currents that are produced by small and moderate voltages low.
If skin becomes wet, however, its resistance is lower, and the electric current can rise to dangerous levels.
A current as low as 1 mA can be felt as a mild shock, while currents of 15 mA can cause loss of muscle control, and currents of 100 mA can cause death.
Current Through a Resistor Example
A 30.0-V battery is connected to a 10.0-Ω resistor. What is the current in the circuit?
Step 1:
Draw a circuit containing a battery, an ammeter, and a resistor.
Show the direction of the conventional current.
Step 2:
Known: V = 30.0 V, R = 10.0 \Omega
Unknown: I = ?
Use I = V/R to determine the current.
I = (30.0 V) / (10.0 \Omega) = 3.00 A
Step 3:
Current is measured in amperes.
With a fairly large voltage and a small resistance, a current of 3.00 A is reasonable.
Parallel and Series Connections
When a voltmeter is connected across another component, it is called a parallel connection because the circuit component and the voltmeter are aligned parallel to each other in the circuit.
Any time the current has two or more paths to follow, the connection is labeled parallel.
The potential difference across the voltmeter is equal to the potential difference across the circuit element.
Always associate the words voltage across with a parallel connection.
An ammeter measures the current through a circuit component.
The same current going through the component must go through the ammeter, so there can be only one current path.
A connection with only one current path is called a series connection.
To add an ammeter to a circuit, the wire connected to the circuit component must be removed and connected to the ammeter instead.
Then, another wire is connected from the second terminal of the ammeter to the circuit component.
In a series connection, there can be only a single path through the connection.
Always associate the words current through with a series connection.
22.2 Using Electrical Energy
Main Idea
Electrical energy can be transformed to radiant energy, thermal energy, and mechanical energy.
Essential Questions
How is electrical energy transformed into thermal energy?
How are electrical energy and power related?
How is electrical energy transmitted with as little thermal energy transformation as possible?
Review Vocabulary
Thermal energy: the sum of the kinetic and potential energies of the particles in an object.
New Vocabulary
Superconductor
Kilowatt-hour
Electrical Energy, Resistance, and Power
Energy that is supplied to a circuit can be used in many different ways.
A motor converts electric energy to mechanical energy, and a lamp changes electric energy into light.
Unfortunately, not all of the energy delivered to a motor or a lamp ends up in a useful form.
Some of the electric energy is converted into thermal energy.
Some devices are designed to convert as much energy as possible into thermal energy.
Current moving through a resistor causes it to heat up because flowing electrons bump into the atoms in the resistor.
These collisions increase the atoms’ kinetic energy and, thus, the temperature of the resistor.
A space heater, a hot plate, and the heating element in a hair dryer all are designed to convert electric energy into thermal energy.
These and other household appliances act like resistors when they are in a circuit.
When charge, q, moves through a resistor, its potential difference is reduced by an amount, V.
The energy change is represented by qV.
In practical use, the rate at which energy is changed–the power, P = E/t–is more important.
Current is the rate at which charge flows, I = q/t, and that power dissipated in a resistor is represented by P = IV.
For a resistor, V = IR.
Thus, if you know I and R, you can substitute V = IR into the equation for electric power to obtain the following.
Power is equal to current squared times resistance.
P = I^2R
Thus, the power dissipated in a resistor is proportional to both the square of the current passing through it and to the resistance.
If you know V and R, but not I, you can substitute I = V/R into P = IV to obtain the following equation.
Power is equal to the voltage squared divided by the resistance.
P = V^2/R
Thermal energy is equal to the power dissipated multiplied by the time. It is also equal to the current squared multiplied by resistance and time as well as the voltage squared divided by resistance multiplied by time.
Electric Heat Example
A heater has a resistance of 10.0 Ω. It operates on 120.0 V.
What is the power of the heater?
What thermal energy is supplied by the heater in 10.0 s?
Step 1:
Sketch the situation.
Label the known circuit components, which are a 120.0-V potential difference source and a 10.0-Ω resistor.
Step 2:
Known: R = 10.0 \Omega, V = 120.0 V, t = 10.0 s
Unknown: P = ?, E = ?
Because R and V are known, use P = V^2/R.
P = (120.0 V)^2 / (10.0 \Omega) = 1.44 kW
Solve for the energy: E = Pt
E = (1.44 kW)(10.0 s) = 14.4 kJ
Step 3:
Power is measured in watts, and energy is measured in joules.
For power, 10^2 * 10^2 * 10^{-1} = 10^3, so kilowatts is reasonable.
For energy, 10^3 * 10^1 = 10^4, so an order of magnitude of 10,000 joules is reasonable.
Superconductors
A superconductor is a material with zero resistance.
There is no restriction of current in superconductors, so there is no potential difference, V, across them.
Because the power that is dissipated in a conductor is given by the product IV, a superconductor can conduct electricity without loss of energy.
At present, almost all superconductors must be kept at temperatures below 100 K.
The practical uses of superconductors include MRI magnets and in synchrotrons, which use huge amounts of current and can be kept at temperatures close to 0 K.
Providing Electrical Energy
Hydroelectric facilities are capable of producing a great deal of energy.
This hydroelectric energy often must be transmitted over long distances to reach homes and industries.
How can the transmission occur with as little loss to thermal energy as possible?
Electrical energy is transformed at a rate represented by P = I^2R.
Electrical engineers call the resulting unwanted thermal energy the Joule heating loss, or I^2R loss.
To reduce this loss, either the current, I, or the resistance, R, must be reduced.
All wires have some resistance, even though their resistance is small.
The large wire used to carry electric current into a home has a resistance of 0.20 Ω for 1 km.
Suppose that a farmhouse was connected directly to a power plant 3.5 km away.
The resistance in the wires needed to carry a current in a circuit to the home and back to the plant is represented by the following equation:
R = 2(3.5 km)(0.20 \Omega/km) = 1.4 \Omega
An electric stove might cause a 41-A current through the wires.
The power dissipated in the wires is represented by the following relationships:
P = I^2R = (41 A)^2 (1.4 \Omega) = 2400 W
All of this power is converted to thermal energy and, therefore, is wasted.
This loss could be minimized by reducing the resistance.
Cables of high conductivity and large diameter (and therefore low resistance) are available, but such cables are expensive and heavy.
Because the loss of energy is also proportional to the square of the current in the conductors, it is even more important to keep the current in the transmission lines low.
How can the current in the transmission lines be kept low?
The electric energy per second (power) transferred over a long-distance transmission line is determined by the relationship P = IV.
The current is reduced without the power being reduced by an increase in the voltage.
Some long-distance lines use voltages of more than 500,000 V.
The resulting lower current reduces the I^2R loss in the lines by keeping the I^2 factor low.
Long-distance transmission lines always operate at voltages much higher than household voltages in order to reduce I^2R loss.
The output voltage from the generating plant is reduced upon arrival at electric substations to 2400 V, and again to 240 V or 120 V before being used in homes.
While electric companies often are called power companies, they actually provide energy rather than power.
Power is the rate at which energy is delivered.
When consumers pay their home electric bills, they pay for electric energy, not power.
The amount of electric energy used by a device is its rate of energy consumption, in joules per second (W) times the number of seconds that the device is operated.
Joules per second times seconds, (J/s)s, equals the total amount of joules of energy.
The joule, also defined as a watt-second, is a relatively small amount of energy, too small for commercial sales use.
For this reason, electric companies measure energy sales in a unit of a large number of joules called a kilowatt-hour, kWh.
A kilowatt-hour is equal to 1000 watts delivered continuously for 3600 s (1 h), or 3.6 \times 10^6 J.