Chapter 17 Electrical Energy and Current

17.1 Electric Potential Electrical Potential Energy When two charges interact, there is an electric force. This is similar to gravitational force and creates potential energy. Electrical potential energy results from the interaction of the charges, not masses.

Electrical potential energy is a component of mechanical energy Recall, any time a force is used to move something, work is done on that object. When an electric force moves charges, work is also done. In this photo, electrical potential energy is reduced every time a charge travels outward to the walls. As the charge drops, so does electrical PE.

Electrical potential energy can be associated with a charge in a uniform field A uniform field is a field that has the same value and direction at all points. Charge is displaced at a constant velocity in the same direction as the electric field. The negative sign indicates that the electrical potential energy will increase if the charge is negative. This potential “difference” is what is important here.

Electrical potential energy is similar to gravitational potential energy After any charge movement, like with gravity, the potential energy is less. When a charge moves perpendicular to “E” no work is done, just like moving horizontal to gravity, no work is done then either. In this example, the only work done is the distance traveled (d). Electrical potential energy

Potential Difference If the size of the charge increases, so does the potential energy. “Electrical potential” is the work that must be performed against electric forces to move a charge from one reference point to another divided by charge. This equals a “volt” (V) …

Potential difference is a change in electric potential “Potential difference” is the work that must be performed against electric forces to move a charge between two points, divided by the charge. This “change” in electrical position is called the volt. It is also equivalent to one joule per coulomb. A battery can range from 1.5 to 13.2 V. Another way to think of this is a change in energy per unit of charge.

The potential difference in a uniform field varies with the displacement from a reference point To simplify the potential energy equation, we can combine it with the expression for electrical potential energy.  As the charge moves in the electric field, the potential difference can be expressed as… Keep in mind “d” is the displacement parallel to the field. Any movement perpendicular does not change the electrical potential energy. potential difference

The reference point for the potential difference near a point charge is often at infinity To determine the potential difference between two points in the field of a point charge, calculate the electrical potential associated with each point. (B) is responsible for the electrical potential at (A). The potential exists at some point regardless of whether there is a charge there or not. The potential of the point depends on the charge responsible and the distance.

The superposition principle can be used to calculate the electric potential for a group of charges Just like with finding the resultant electric field at a point in space, finding electrical potential are only scalar quantities. To evaluate the electrical potential at a point near a group of charges, you just take the algebraic sum but you must keep track of the signs (+ and -) superposition principle

Practice A Potential Energy and Potential Difference A charge moves a distance of 0.020 m in the direction of a uniform electric field whose magnitude is 215 N/C. As the charge moves, its electrical potential energy decreases by -6.9 x 10-19 J. Find the charge on the moving particle (q = ?) What is the potential difference between the two locations (∆V = ?)

Given: ∆PEelectric = -6.9 x 10-19 J d = 0.020 m E = 215 N/C Unknown: q =? and ∆V = ? For electrical potential energy use…  Answer For potential difference use… 1.6 x 10-19 C -4.3 V

A battery does work to move charges A battery is an energy storage device that provides a constant potential difference between two locations called terminals. A 1.5 V battery maintains a potential difference across its terminals such that the positive terminal has an electrical potential that is 1.5 V higher than the negative. Inside the battery a chemical reaction produces electrons that move through the battery and collect on the negative terminal. For every coulomb of charge that leaves the positive terminal = 1.5 J of electrical potential energy. If no electrons are allowed to travel to the positive terminal, the battery can hold its charge for some time.

Questions 1. T / F When an electric force moves charges, work is also done. 2. In a uniform field, charge is displaced at a ________ velocity in the same direction as the electric field. 3. After any charge movement, like with gravity, the potential energy is ( more / less )? 4. Change in electrical position is called the ____. It is also equivalent to one joule per coulomb. 5. Inside the battery a chemical reaction produces _______ that move through the battery and collect on the negative terminal. true constant ___ volt electrons

17.2 Capacitance Capacitors and Charge Storage A capacitor is a device that is used to store electrical energy. Examples include; flash bulbs and keyboards. An energized capacitor is useful because energy can be reclaimed when needed. A capacitor consists of two metal plates separated by a small distance… Charge Storage

…this is known as the parallel plate capacitor. The capacitor is energized by connecting the plates to two terminals of a battery. Once charged, the plates have an equal and opposite charge. Capacitors

Capacitance is the ratio of charge to potential difference The ability of a conductor to store energy in the form of electrically separated charges is measured by capacitance. Capacitance is the ratio of the net charge on each plate to the potential difference created by the separated charges. The SI unit for capacitance is the farad, F. Named after physicist Michael Faraday. A farad is equal to one coulomb per volt. C = capacitance A = area of one plate d = distance between plates

Capacitance depends on the size and shape of the capacitor Some parallel plate capacitors have no medium between them and exist in a vacuum. To represent the permittivity of the medium, we use the Greek letter epsilon, ε. In the case of a vacuum, we use the constant 8.85 x 10-12 C2 /Nm2

The material between a capacitor’s plates can change its capacitance When the space between the capacitor’s plates is not a vacuum, it can contain a material called dielectric. Examples include; air, rubber, glass or even wax paper. When a capacitor has a dielectric material, it increases the capacitance. The dielectric reduces the charge on the plates allowing it to store more charge for a given potential difference.

Discharging a Capacitor releases its charge Once a capacitor is charged, it no longer needs a power source. This allows the capacitor to remain charged. Once a connection between the plates occurs, the capacitor will discharge. A Camera flash works on this same principle. That is why it takes a few seconds for the flash to be available again. Computer circuits recognize that a key on the keyboard has been depressed due to this discharge.

Energy and Capacitors A charged capacitor stores electrical potential energy because it requires work to move charges through a circuit to the opposite plate. Once a charge has been transferred, a small potential difference appears between the plates. The electrical potential energy stored in a capacitor that is charged from zero to some charge, Q, is given by the following…

This equation is also an expression for the work required to charge the capacitor. There is a limit to the maximum energy (or charge) that can be stored. Electrical breakdown in a capacitor is like a lightning discharge. Too much potential difference and zap!

Practice B Capacitance A capacitor, connected to a 12 V battery, holds a 36 µC of charge on each plate. What is the capacitance of the capacitor? How much electrical potential energy is stored in the capacitor?

Given: Q = 3.6 ×10-5 C ∆V = 12 V Unknown: C =? and PEelectric =? Answer use this answer for “C” below… Answer 3.0 x 10-6 F 2.2 x 10-4 J

Questions 1. T / F An energized capacitor is useful because energy can be reclaimed when needed. 2. Once charged, the plates have an equal and ________ charge. 3. When the space between the capacitor’s plates is not a vacuum, it can contain a material called ________. 4. When a capacitor has a dielectric material, it ( increases / decreases ) the capacitance. 5. Once a connection between the plates occurs, the capacitor will _________. true opposite dielectric ________ discharge

17-3 Current and Resistance Current and Charge Movement The movement of electric charge is known as current. Electrical current is needed for our lights, radios and the components that make up the chips of computers. Electric currents are even part of the human body. Since the late 1700’s we have known that an animal’s nervous system is initiated by electrical activity.

Current is the rate of Charge Movement A current exists whenever there is a net movement of electrical charge through a medium. Current (I) is the ratio of the amount of charge to the interval. The direction of current is opposite the movement of the negative charges. The SI unit for current is the ampere (A). It is equivalent to one coulomb passing a point in a second. (CIA)

Practice C Current The current in a light bulb is 0.835 A. How long does it take for a total charge of 1.67 C to pass through the filament of the bulb? Given: Q = 1.67 C and I = 0.835 A Unknown: t = ?  Answer 2.00 s

Conventional current is defined in terms of positive charge movement Current is due to the motion of negatively charged electrons. This can occur in the structure of solid conductors. It allows the electrons to transfer easily from one atom to the next. Positive and negative charges in motion are sometimes called charge carriers. Conventional current is defined in terms of the flow of positive charges, even though the electrons are moving in the opposite direction.

For a material to be a good conductor, charge carriers in the material must be able to move easily. Many metals usually contain a large number of free electrons. Body fluids and salt water are able to conduct electric charge because they contain charged atoms called ions. A water solution that conducts an electric current is called an electrolyte.

Drift Velocity When you flip a light switch, the lights come on almost immediately. However, this is not because electrons move really fast. In fact, it is the propagation of change that moves through the wire quickly not the actual electron charges. The electrons actually move quite slowly.

Drift velocity is the net velocity of the charge carriers When the conductor is in electrostatic equilibrium, the electrons move randomly. When a potential difference is applied across the conductor, an electric field is set up inside the conductor. This force, due to a field, sets the electrons in motion creating a current. These electrons do not move in straight lines, they undergo repeated collisions. This can cause an increase in temperature. Despite these collisions, they move in a direction opposite the electric field “E”, at a velocity known as drift velocity. Drift Velocity

Drift speeds are relatively small Drift speeds are typically small. To travel only one meter could take the electrons 68 minutes! On the other hand, the electric field reaches across the electrons in the wire at a speed close to the speed of light! Think about the water coming out of a hose. You open the valve and if there is already some water in the hose, pressure is felt at the other end almost immediately.

Resistance to Current The opposition to the motion of charge through a conductor is the conductor’s resistance. The SI unit for resistance is the ohm. It is equal to one volt per ampere. The symbol for resistance is the Greek letter omega () R = resistance () “ohm” V = potential difference I = current

Resistance is consistent over a range of potential differences When resistance is consistent over a range of applied potential differences, this is known as ohm’s law. Ohm’s law is usually shown as…

Ohm’s law does not hold for all materials Only certain materials follow Ohm’s law. If they do, they are said to be ohmic. The straight line shows this. Materials that do not follow Ohm’s law do not have a straight line and are said to be non-ohmic. One common non-ohmic device is the diode. Its resistance is small for currents in one direction and large for currents in the reverse. Diodes are used in circuits to control the direction of current.

Resistance depends on length, area, material, and temperature Factors that affect the number of collisions will also affect a material’s resistance. Below are a number of variables. Warmer materials have atoms that are vibrating faster so this causes the electrons to collide more. Resistance depends on length, cross-sectional area, material, and temperature.

Resistors can be used to control the amount of current in a conductor One way to change the current in a conductor is to change the potential difference across the end of the conductor. You can not do this in your house because all of your outlets are rated for 120 volts. So, to decrease current, you simply allow more resistance. Electronics have built in resistors as shown is the upper photo.

Practice D Resistance The resistance of a steam iron is 19.0 Ω. What is the current in the iron when it is connected across a potential difference of 120 V? Given: R = 19.0 Ω ∆V = 120 V Unknown: I = ? Answer 6.32 A

Salt water and perspiration lower the body’s resistance The human body’s resistance to current is on the order of 500,000 Ω when the skin is dry. Salt water can lower your resistance down to as much as 100 Ω. Ions in salt water readily conduct electric charge. These low resistances can be dangerous. Currents of 0.01 A can hardly be felt by humans. Currents more than 0.15 A can cause possible death!

Potentiometers have variable resistance A potentiometer is a special type of resistor that is adjustable. As you turn the knob one way or the other changes the amount of resistance allowing light, sound, or any other source of power to go up or down.

Questions 1. The movement of electric charge is known as _______. 2 Questions 1. The movement of electric charge is known as _______. 2. The direction of current is ( opposite / same as ) the movement of the negative charges. 3. The opposition to the motion of charge through a conductor is the conductor’s _________. 4. A _____ in circuits control the direction of current by making resistance small in one direction and large in the reverse. 5. T / F Since most electronics do not need the same voltage, they have built in resistors to decrease current. current _______ resistance diode true

17.4 Electrical Power Sources and Types of Current Drop a ball from a higher place and gravitational potential energy moves it downward. Potential difference applied across the conductor moves charges from higher electrical potential to a lower one. Thus, potential difference maintains current in a circuit.

Batteries and generators supply energy to charge carriers Batteries maintain a potential difference across their terminals by converting chemical energy to electrical potential energy. As charge carriers move from higher to lower electrical potential energy, this energy is converted to kinetic energy. This motion causes collisions that create heat in the system. Energy is released through chemical reactions that occur inside the battery.

Generators convert mechanical energy into electrical energy. A hydroelectric power plant converts its kinetic energy of falling water into electrical energy. Coal burning plants make steam that turns turbines that then turn generators. Nuclear power plants use the heat from radiation to make steam. If you use electricity in your home, it most likely came from one of these 3 sources.

Current can be direct or alternating There are two types of current, direct (dc) and alternating (ac). In direct current, charges move only in one direction with negative charges moving from lower to higher electrical potential. The conventional current is directed from the positive terminal to the negative. Remember, the electrons move in the opposite direction.

In alternating current, the source of potential difference constantly changes sign. There is no net motion of the charge carriers, they simply vibrate back and forth. If this vibration were slow enough, you would see your lights flicker. To avoid this, the change occurs 60 times a second. One big advantage of alternating current is that it can be transported long distances.

Energy Transfer When a battery is used to maintain an electric current, chemical energy stored in the battery is continuously converted to the electrical energy of the charge carriers. The light bulb filament (B-C) has a higher resistance than the wire. When the charge returns to the battery (D-A) its electrical potential is increased by Q∆V. Electrical energy

Electric power is the rate of conversion of electrical energy Power is the rate at which work is done. Electric power is the rate at which charge carriers do work. So one watt (W) is equivalent to one (J) of electrical energy being converted to other forms of energy per second. The amount of heat and light given off by a light bulb is known as the wattage of the bulb. Joule heating is also known as I 2 R loss.

Practice E Electric Power An electric heater is connected across a 120 V outlet. The heater dissipates 1320 W of power in the form of electromagnetic radiation and heat. Calculate the resistance of the heater. Given: V = 120 P = 1320 W  Unknown: R = ? Answer 10.9 Ω

Electric companies measure energy consumed in kilowatt-hours Power companies charge for energy, not power. The unit of energy used by electric companies to calculate consumption is the kilowatt-hour. One kilowatt-hour (kW h) is the energy delivered in one hour at a constant rate of 1 kW. 1 kW h = 3.6 X 106 J An electric meter outside your house measures the energy you have consumed over a period of time. Kilowatt hours

Electrical energy is transferred at high potential differences to minimize energy loss Power companies what to minimize the I 2 R loss and maximize the energy delivered to the customer. Wires have little resistance, but over great distances it becomes an issue. P = I 2 R Because of this formula, low currents and high potential differences (V) lowers the amount of energy lost. Wires can transport power at voltages of 760,000, then lower them to 4000, and then again down to 120 for your home using transformers.

Questions 1. Potential difference applied across the conductor moves charges from higher electrical potential to a lower one, this maintains ______ in a circuit. 2. Batteries maintain a potential difference across their ________ by converting chemical energy to electrical potential energy. 3. __________ convert mechanical energy into electrical energy, like at a power plant. 4. In ( AC / DC ) current, there is no net motion of the charge carriers, they simply vibrate back and forth. 5. One kilowatt-hour (kW h) is the energy delivered in one ____ at a constant rate of 1 kW. current terminals Generators ___ hour

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