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Ch. 17 Current and Resistance concept #1, 4, 5, 6, 8, 10 Problems #1, 2, 3, 7, 11, 13, 17, 21, 25, 27, 31, 33, 43 Static electricity devices, such as a Van de Graaf generator, produced small flow of charge for short time intervals. When it was learned how to produce a continuous flow for longer times, electricity became an important part of human technology. For example run a light bulb, use to power a refrigerator. The continuous flow of charge leads up to electric current. Take a wire and cut a cross sectional area through it. The charges move in a direction perpendicular to the surface. Current – the rate at which charge flows through the surface. The current is the amount of charge Q that flows through a cross-sectional area in a time interval t. Current: I = Q/ T SI unit of current is the Ampere (A) 1 Ampere = 1 coulomb/second A = C/s Direction of current: The direction of the current is the direction in which positive charges flow. Remember that in a conductor, the charges that move are the negative electrons. So in a copper wire, the current is in the opposite direction of the electron’s motion. e current Take the example of a current loop. If the electrons flow clockwise. The current is counterclockwise. A particle accelerator shoots a beam of protons. The current is in the same direction of the protons’ motion. see example problem 17.1 Microscopic view of current The current depends on the average speed of the charge carriers. Not all the electron will move with the same speed. I = Q/ t Q = number of carriers x charge per carrier = (nA x)q n charge density (#/volume) A = cross-sectional area x = length along wire q = charge of individual carrier for electron (q = 1.6 x 10-19 C) Q = (nA x)q a distance x = vd t vd = drift velocity (average velocity along direction of motion) see picture (pg 570) Q = (nA vd t)q I = Q/ t = (nA vd t)q / t = (nA vd)q I = nqvdA Work example 17.2. As charges flow through a conductor (wire), they are constantly colliding with each other and the walls of the conductor. It is the net movement of charge that produces the current. Think of water through a pipe. If a drop of water is forced into an already filled pipe, a drop will be pushed out the other end. A current flow at one end produces a similar flow at the other end very quickly. Current and voltage measurement in circuits. circuit – closed loop of some sort around which current circulates Basic circuit – battery hooked to a light bulb. The battery pushes the charges through the light bulb and around the loop. Circuits need closed loops for current to flow. Current won’t flow through a ‘dead end’. The battery increases the potential energy of the charges. Then the charges lose the PE as they go around the circuit. Think of the circuit as a roller coaster that the charges ride. The initial ‘lift’ that the charges need to get over the hill is provided by the battery. measuring devices voltmeter – measures voltages (potential differences) ammeter – measures the current See fig 17.5 voltmeters always need to be in parallel ammeters always need to be in series Resistance and Ohm’s law When a voltage is applied across a conductor, current will flow and will be proportional to the potential difference. I~ V The proportionality constant is known as the resistance. Resistance is defined as the ratio of the voltage across a conductor to the current it carries. R = V/I resistance has units of volts per ampere Called Ohm’s ( ) 1 V/1 A = 1 Ohm’s Law: V = I R Can compare electrical current to current in a river. - as river’s change in elevation increases, the current increases (the potential difference increases) - if river is blocked up with rock, the flow decreases (similar to having a larger resistance) Resistor Symbol is a zigzag material is ohmic if the resistance is constant over a large range of voltages nonohmic – resistance changes with voltage see graphs on pg 574 example 17.3 Resistivity Resistance depends on the length and width of the conductor. As electrons move through the conductor, they bounce into the atoms in the material. The more collisions, the higher the resistance. if you want to minimized the collisions, use a short and wide conductor. wider – lower resistance longer – higher resistance. Resistance is proportional to the length and inversely proportional to the cross-sectional area. The proportionality constant is the resistivity. R = L/A The resistivity has units of m Resistivity depends on what the conductor is made out of. Switching to a high resistance. material will increase Good conductors have small resitivities. see table 17.1 (pg 576) example 17.4 Temperature variation of resistance. Resistance depends on resistivity. Resistivity depends on atomic structure. Atomic spacing depends on temperature. = 0{1 + (T – T0)} = temperature coefficient of resistivity (how the resistivity changes with temperature) Second column of table on page 576. Sine resistivity changes with temperature, so does resistance. R = R0{1 + (T – T0)} and R0 are the resistivity and resistance at a reference temperature T0. 0 When you increase the temperature of a resistor, the resistance increases. Superconductors Resistance increases with temperature. Low temp, low resistance. For some metals, there is a critical temperature, Tc, where the resistance drops to zero. If R = zero, then an established current will flow without an applied voltage. Goal is to produce superconductors at higher and higher temperatures. Electrical Energy and Power As charge moves around circuit, it increases in potential as it goes through battery, then loses potential as it goes through resistor. When it returns to original point it is back at original potential. Remember that there are collisions between the charge and the atoms in the resistor. This causes the resistor to gain thermal energy. The potential energy is turned into thermal energy. As charge passes through resistor, the charge, Q, loses an amount of potential energy Q V. If it takes time, t, to pass through the resistor, the rate that the charge loses potential energy is: Q V/ t = ( Q/ t)DV = I V power is current x potential difference P=IV Using Ohm’s law we can make subtitutions and see: P = I V = I2R = V2/R Do examples 17.6 and 17.7a units SI unit of energy is the Joule (J) SI unit of power is the Watt (W) Power = energy/time Unit used by electric companies is the: kilowatt-hour. This is a unit of energy. 1 kWh = using 1000 W for 1 hour of time 1kWh = (103 W)(3600 s) = 3.6 x 106 J