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Chapter 17: Electrical Energy and Current1 Section 1: Electric Potential Electric Potential Energy When 2 charges interact, there is an electric force between them. Also an electrical potential energy – results from the interaction of two objects’ charges, not their masses Component of mechanical energy ME is conserved as long as friction and radiation are not present ME = KE + PEgrav + PEelastic + PEelectric Remember: any time a force is used to move an object, work is done on the object True for charges moved by electric force Whenever a charge moves because of the electric field produced by another charge(s), work is done on the charge that moves Tesla Coil – contains a plate in the center where negative electric charges build up. Electrical potential energy of each charge decreases as the charge moves from the plate to the walls, and then to the ground Electrical potential energy Consider a positive charge in a uniform electric field. The charge is displaced at a constant velocity in the same direction as the electric field. A uniform electric field is a field that has the same value and direction at all points. Change in the electrical potential energy associated with the charge’s new position in the electric field. Change depends on the charge, q strength of the electric field, E displacement, d ΔPEelectric = -qEΔd Electric PE = —(charge x electric field strength x displacement from a reference point in the direction of the field) Negative sign indicates that the PE will increase if the charge is negative and decrease if the charge is positive. Chapter 17: Electrical Energy and Current2 Like all forms of potential energy … It is the difference in electrical potential energy that is important o If the initial position is chosen as a reference point (zero level), then the initial electrical potential energy is zero, which changes the equation to: ΔPEelectric = -qEd o Equation only works in a uniform electric field o d is the magnitude of the displacement’s component in the direction of the electric field o Any displacement perpendicular to the field does not change PEelectric SI unit for PEelectric is the joule (J) Think about gravitational potential energy: Gravitational field is vertical Only movement parallel to the gravitational field affects PEg. All other movement perpendicular (horizontal) to the field has no effect. Work and potential energy Remember, W = Fd Electric field does work on a positive charge by moving the charge in the direction E o Final potential energy is less than initial PE o Negative charge is opposite – negative charge undergoes a force in the opposite direction Potential Difference Electrical potential energy increases as the magnitude of the charge increases. Electric potential allows us to express the potential energy in a way that is independent of the test charge. Electric potential: electrical potential energy associated with a charged particle in an electric field divided by the charge of the particle V = PEelectric Unit: volt, V, = J/coulomb q Potential difference is a measure of the difference in the electrical potential energy between 2 positions in space divided by the charge. Chapter 17: Electrical Energy and Current3 Potential difference is a change in electric potential energy As a 1 C charge moves through a potential difference of 1 V, the charge gains 1 J of energy Electric potential is represented by V Potential difference (change in electric potential) is represented by ΔV and is sometimes referred to as voltage. Reference point for measuring electrical potential energy is arbitrary Reference point for measuring electrical potential is also arbitrary o Only changes in electric potential is significant Electrical potential energy is a quantity of energy, measured in joules o Both electric potential and potential difference are both measures of energy per unit charge, measured in volts o Potential difference describes a change in energy per unit charge Potential difference in a uniform field varies with the displacement from a reference point Combining the equation for potential difference with the equation for electrical potential energy results in equations that are simpler to apply in some situations. PEelectric = —qEd ΔV = ΔPEelectric = Δ(—qEd) q q As the charge moves in a uniform electric field, the quantity in the parentheses does not change from the reference point. Potential difference in a uniform electric field ΔV = —Ed Potential difference = —(magnitude of the electric field x displacement) d is the displacement parallel to the field motion perpendicular to the field does not change the electrical potential energy. Reference point for potential difference near a point charge is often at infinity To calculate the potential difference between 2 points in the field of a point charge: [scenario: point charge q2 at point A in the electric field of a point charge q1 at point B, r distance away] 1. Calculate the electric potential associated with each point: VA = PEelectric = kCq1q2 = kCq1 q2 rq2 r a. Keep up with the 2 charges and don’t confuse them. q1 is responsible for the electric potential at point A. b. An electric potential exists at some point in an electric field regardless of whether there is a charge at that point. Chapter 17: Electrical Energy and Current4 Continuing on with the example … 2. Electric potential at a point depends only on the charge responsible for the electric potential, and the distance, r, from this charge to the point in question. a. If the 2 distances are r1 and r2, then the potential difference between these 2 points is: 𝟏 𝟏 ΔV = kCq1 — kCq1 = kCq1 𝒓𝟐 − 𝒓𝟏 r2 r1 b. If the distance r1 is large enough, it is assumed to be infinitely far from the charge q1. If so, then 1/r1 is considered to be zero. 3. Equation becomes: ΔV = kCq r potential difference = Coulomb constant x value of the point charge distance to the point charge This equation looks identical to the one for electric potential associated with a point charge because we have chosen a special reference point from which to measure the potential difference. 4. Application for potential difference is the operation of electric circuits. The reference point for determining electric potential is arbitrary and must be defined. a. Earth is frequently designated as having an electric potential of zero b. When an electrical device is grounded (connected to Earth), a possible reference point is created which allows you to measure the electric potential in an electric circuit. Sample 17A A charge moves a distance of 2.0 cm 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 10-19J. Find the charge on the moving particle. What is the potential difference between the two locations? Chapter 17: Electrical Energy and Current5 Superposition principle Can be used to calculate the electric potential for a group of charges o The total electric potential at some point near several point charges is the sum of all the electric potentials from each charge o Summation here is easier than with electric field because these are scalar, not vector, quantities. o Keep track of signs – the electric potential near a positive charge is positive; near a negative charge is negative. Battery does work to move charges Battery – energy-storage device; provides a constant potential difference between its two terminals. AA battery: + terminal has a potential difference of 1.5 V higher than the potential difference of the — terminal. Chemical reaction produces electrons (negative charges) that collect on the negative terminal. o Chemical reaction does work on the charges when moving them from the positive to the negative terminal o Every coulomb of charge that leaves the + terminal has 1.5 J of electrical potential energy Negative charges move from the positive to the negative terminal through a potential difference of ΔV = -1.5 V. When in an electrical device, 1 C of charge moves through the device toward the positive terminal of the battery o 1.5 J of electrical is given to the device o When the charge reaches the + terminal, the charge’s electrical potential energy = 0. o Electrons return to the + terminal for the chemical reaction to occur. http://regentsprep.org/Regents/physics/phys03/apotdif/default.htm Section 2: Capacitance Terms: Capacitor: device used to store electrical potential energy. Energized (or charged) capacitor: charged capacitor whose energy can be used for a specific purpose. Parallel-plate capacitor: typical design of a capacitor consisting of 2 metal plates separated by a small distance. Charge refers to the magnitude of charge on either plate. Chapter 17: Electrical Energy and Current6 Capacitance expresses how much charge the capacitor plates have relative to the potential difference between the plates. The farad (F) is named for Michael Faraday. Most capacitors have capacitances ranging from microfarads (1x10-6 F)to picofarads (1x10-12 F) ε (epsilon) represents permittivity of the medium (how responsive the medium is to an electric field). ε0 indicates a vacuum and has a magnitude of 8.85 x 10-12C2/N•m2 Capacitance: ability of a conductor to store energy in the form of electrically separated charges. Ratio of the net charge on each plate to the potential difference created by the separated charges C=Q measured in C/V (also called the farad, F) ΔV Capacitance = magnitude of charge on each plate potential difference Capacitance Capacitance of a parallel-plate capacitor with no material between the plates is determined by: C = ε0A d Capacitance = permittivity of a vacuum x area of one plate distance b/t plates Combining capacitance with equation for charge: Q = ε0AΔV d From this equation, we learn: For a given potential difference (ΔV), the charge on the plate is proportional to the area of the plates and inversely proportional to the distance (separation) between the plates. Chapter 17: Electrical Energy and Current7 Material between the plates of a capacitor can change its capacitance. Dielectric – material occupying the space between the plates of a parallel-plate capacitor. Insulating material (such as air, rubber, glass, or waxed paper) Capacitance increases with dielectric o Plates can store more charge for a given potential difference o Problems in our book assumes no dielectrics (ε0) Discharging a capacitor 1. Charge a capacitor by connecting it to a battery a. Once charged, the battery can be removed b. Capacitor will hold its charge until connected to a circuit 2. Connect a capacitor to a circuit and it will discharge a. Ex. Flash in a camera i. Faster than using a battery b. Ex. Computer keyboard Energy and Capacitors A charged capacitor stores electrical potential energy because it requires work to move charges through a circuit to the opposite plates of a capacitor. Initially uncharged, both plates are neutral Requires almost no work to move a small amount of charge Once charge has been transferred, a small potential difference exists between the plates Requires more work to move additional charge through the potential difference, so electrical potential energy increases Electrical potential energy stored in a capacitor that is charged from zero to some charge, Q: PEelectric = ½QΔV Using the equation C = Q/ΔV, we get the following alternative forms: PEelectric = ½C(ΔV)2 PEelectric = Q2 2C Sample 17B A capacitor, connected to a 12 V battery, holds 36 µC of charge on each plate. What is the capacitance of the capacitor? How much electrical potential energy is stored in the capacitor? Chapter 17: Electrical Energy and Current8 Section 3: Current and Resistance Current and charge movement Sample 17C Current – movement of electric charge 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? Technology Appliances Bodies! (electric currents transmit messages between body muscles and the brain) Electric current – rate at which charges move through a cross section of wire I = ∆Q ∆t Electric current moves opposite the movement of the negative charges. measured in ampere, A = 1C/s Electric current = charge passing area time interval Conventional current Moving charges that make up a current can be: Negative (moving electrons in solid conductors) Positive (protons are set in motion in particle accelerators) Combination (in gases and dissolved salts, + charges move in one direction, ― charges move in the opposite direction Positive and negative charges in motion are called charge carriers. Conventional current is defined in terms of the flow of positive charges. Negative charge carriers (electrons) would have a conventional current opposite their physical motion. Electric field in a material sets charges in motion. Conductors: charge carriers move easily Metals – large number of free electrons Body fluids – contain ions Electrolytes – solute that dissolves in water and conducts electric charge Chapter 17: Electrical Energy and Current9 Drift Velocity You turn on a light switch, and light appears almost instantly. Many people believe that electrons must flow very rapidly from the switch to the bulb for the light to appear so quickly. This is NOT true! Electron motion near the switch changes the electric field there Change in the electric field moves through the wire very rapidly o Nearly the speed of light o Charges move more slowly When a potential difference is applied across a conductor, the electrons do not move in straight lines in the opposite direction of the electric field. Repeated collisions with the vibrating atoms of the conductor Energy transferred from the electrons to the metal atoms increases the vibrational energy of the atoms Conductor’s temperature increases Electrons gain kinetic energy as they are accelerated by the electric field Electrons lose kinetic energy because of the collisions Individual electrons move slowly along the conductor, in the opposite direction of the electric field velocity is known as the drift velocity, vdrift Drift speeds are very small o Ex. 10.0A of current, drift speed is 2.46 x 10-4 m/s it would take 68 minutes to move 1 meter! Resistance In a circuit of a light bulb connected to a battery: Battery determines the potential difference that lights the bulb Current in the bulb causes the bulb to light Wires (conductors) and the filament in the bulb also affect the current reaching the bulb and the brightness of the light Resistance: opposition to the motion of charge through a conductor Resistance = potential difference current R = ∆V I unit: ohm (Ω) = V/A Ohm’s Law: Resistance is constant over a wide range of applied potential differences. ∆V = constant I Can also be expressed as ∆V = IR Chapter 17: Electrical Energy and Current10 Ohm’s law Resistance Ohm’s law is not a fundamental law of nature Resistance occurs because of the internal collisions between the charges as they are moved along by the potential difference. Valid only for certain materials Materials with a constant resistance over a wide range of potential differences are ohmic o Graph of current versus potential difference is linear o I/∆V (inverse of Ohm’s law) is inversely proportional to resistance o Non-ohmic materials have a graph that is curved (not constant); resistance varies. Diode (small resistance for currents in one direction; large resistance for currents in the opposite direction Diodes are used in circuits to control the direction of current Internal friction Factors that affect resistance: Length – longer has greater resistance Cross-sectional area – (skinny has greater resistance) Temperature – higher temperature = greater resistance Material Resistors – Ways to adjust the current in a conductor: When potential difference (∆V) remains constant: Current decreases when resistance increases o Replace the wire with one of greater resistance o Use a longer, thinner wire o Connect a resistor to the circuit A simple electrical element that provides a specified resistance Chapter 17: Electrical Energy and Current11 Sample 17D Human Body 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? When dry, human skin has a resistance of 500,000 Ω When wet, specifically soaked in salt water, human skin has a resistance as low as 100 Ω o Ions in salt water readily conduct electric charge Danger exists if a large potential difference is applied between parts of the body because current increases as resistance decreases. Specifics Current level Probable effect on human body • 1 mA • Slight tingling sensation • 5 mA • Slight shock is felt; can ―let go‖ • 6-30 mA • Painful shock; muscular control is lost. Freezing current or ―let go‖ range. • 50-150 mA • Extreme pain, respiratory arrest, severe muscular contractions. Cannot let go. Death possible. • 1000-4300 mA • Pumping action of the heart ceases. Nerve damage. Death. • 10,000 mA • Cardiac arrest, severe burns, DEATH. Perspiration contains ions that conduct electric charge. Galvanic skin response (GSR), used in stress tests and “lie detector” tests, have a small potential difference set up across the body. When stressed (or lying), perspiration increases and decreases the resistance of the body. Potentiometers Special type of resistor Contains an adjustable, sliding contact that allows the user to adjust resistance Dimmer switches, volume control, game controllers (1 for x direction, 1 for y) Chapter 17: Electrical Energy and Current12 Section 4: Electric Power Sources and Types of Current When a potential difference is applied across a conductor, charges will move from a position of higher electrical potential to a position of lower electrical potential Batteries convert chemical energy to electrical potential energy, which can be converted into kinetic energy o KE allows collisions to occur between the moving charges and the remaining material in the circuit elements o Collisions transfer energy (in the form of heat) back to the circuit. Generators convert mechanical energy into electrical energy o Hydroelectric power plant converts KE of falling water into electrical potential energy Current can be either alternating (AC) or direct (DC). Direct – charges only flow in 1 direction; negative charges move from a lower to higher electric potential o Conventional current is directed from the positive terminal to the negative terminal of the battery o Electrons actually move in the opposite direction Alternating – the terminals of the source of potential difference constantly change sign o No net motion of the charge carriers; the charge carriers vibrate back-forth o If the vibration were slow enough, you would see lights flicker; in the US, AC oscillates 60x/second frequency is 60 Hz. o Current transferred to homes/businesses by power companies is AC Energy Transfer 1. Energy from battery is converted to internal energy due to collisions between charge carriers and other particles in conductor. 2. Disregard the resistance of the connecting wire, and no loss of energy occurs as the charge moves from A to B. 3. B to C, loss of electrical energy due to the resistance in the bulb filament. Chapter 17: Electrical Energy and Current13 Continuing on with the circuit 4. In the filament, electrical energy is converted to internal energy; the filament warms up and glows. 5. Charge returns to the battery; potential energy is 0. a. Battery does work on the charge 6. Charge moves between the terminals of the battery (D to A), electrical potential energy increases by Q∆V (where ∆V is the potential difference across the battery terminals. a. Battery’s chemical energy decreases by the same amount. Electrical power is the rate of conversion of electrical energy Electrical power is the rate at which charge carriers do work rate at which charge carriers convert electrical PE to nonelectrical forms of energy P = W = ∆PE ∆t ∆t ∆V = ∆PE ∆PE = q∆V q Substitute equation into power equation: P = q∆V (q/∆t = I), ∆t P = I∆V Electric power = current x potential difference Unit for power is the watt (W) = J/s. How do those units work out? Because ∆V = IR, power can be rewritten in other terms: P = I∆V = I(IR) = I2R P = I∆V = ∆V∆V = (∆V)2 R R Practice 17E An electric space 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. Chapter 17: Electrical Energy and Current14 Electric companies Electric power is the rate of energy transfer. Power companies charge for energy used, not power. Unit of energy used by power companies is the kilowatt-hour (kW•h) o Energy delivered in 1 hour at the constant rate of 1kW Electrical energy to you … Electrical companies want to deliver energy to you with as little loss as possible Conversion of electrical energy to internal energy in a resistant material is called joule heating, and is referred to as an I2R loss (from power formula where ∆V is replaced with IR). Decrease current or resistance o Wires have little resistance, but resistance increases with length o Energy loss is proportional to the square of the current I2R, so decreasing current is more important than decreasing resistance Power can be transported either at high current and low potential difference or vice versa. o To minimize loss, power companies transport electrical energy at very high potential differences (up to 765,000 V). o Transformers reduce the potential difference to about 4000 V o Within our homes, potential difference is reduced again to about 120 V by another transformer.