Chapter 25: Electric Current

Chapter 25: Electric Current

Conductors and Charge Carriers Consider a conducting piece of metal: The valence electrons are weakly bound to the nuclei form a fluidlike sea of electrons that can move through the solid randomly (thermal motion). The atoms are positively charged and remain stationary (ignoring vibrational motion of the solid) The macroscopic charge density of the metal is zero.

Electric Current Electric current is a net flow of electric charge. Current is the rate at which charge crosses a given area. I = dq dt dq = q(n AL)=q(n Av d dt) I = qnav d n is the number of charge carriers per unit volume, each with charge q. v d is the drift velocity, or average velocity of the charge carriers along the direction of the current.

Example What is the drift velocity for 1 Amp of electricity flowing through a 2 mm diameter copper wire? I = enav d v e = I en r 2 v e = 1A (1.67 10 19 C) (8.5 10 28 m 3 ) (10 6 m 2 ) v e =0.022 mm/s

Current density Current density, J, is the current per unit area. J = nqv d Current density may vary with position in both direction and magnitude. The current through an area is the flux of the current density over that area: Z I = ~J da ~ When current density is uniform and perpendicular to a flat area, current becomes the product of current density with area: I = JA

Clicker question CT 29.2a A copper cylinder is machined to have the following shape. The ends are connected to a battery so that a steady, constant current flows through the copper. A B C Which region has the greatest current density J? A, B, C, or D: All three are the same E: Not sure/not enough info?

Derivation of Ohms Law The electrons move about in random directions with high thermal velocities. There s no current associated with thermal motion. An electric field superposes a small drift velocity on the electrons motion. Between collisions electron accelerates due to electric field: Average velocity due to this acceleration is the drift velocity: Microscopic Ohm s law : J = nq v d = ne2 m e E = E a = ( e)e m e v avg = v d a = e m e E

Clicker Question A wire has a constant current I flowing along it. Where is the electric field? 1. E exists along the surface of the wire, but E=0 inside. 2. E exists throughout the wire. 3. E=0 everywhere in the wire since the current isn t changing with time.

CT 29.2d A copper cylinder is machined to have the following shape. The ends are connected to a battery so that a current flows through the copper. A B C Which region has the greatest magnitude electric field E? A, B, C, or D: All three are the same E: Not sure/not enough info?

Ohm s law Recall the microscopic version of Ohm s law: J = E = E Consider a particular piece of conducting material with uniform cross section. How does current relate to voltage across the conductor? V = Z ~E ~dl = EL = JL = I V L A Note: represents magnitude of potential difference across resistor. = IR R is resistance (depends on both material and geometry)

CT 29.3 Two cylindrical resistors are made of the same material (same resistivity). Resistor 2 is twice as long and has twice the diameter of resistor 1. What is the ratio R 2 /R 1? 1 2 A) 2 B) 4 C) 1/2 D) 1/4 E) 1

EMF The Electromotive Force Where does the electric field in a current-carrying conductor come from? What keeps the current flowing over time? An emf device pumps charge from lower to higher potential energy, which maintains the charge separation that produces the E field throughout the circuit. Batteries, electric generators, solar cells, are examples of emf sources.

Clicer Question A charge dq loses potential energy as it goes from one terminal of the battery to the other: U = dq ( V emf ) Where does the energy go? 1. Kinetic energy (drift velocity increases) 2. Thermal Energy 3. Internal potential energy

Electric power A charge dq loses potential energy as it goes from one terminal of the battery to the other: U = dq ( V emf ) Where does the energy go? dissipated as thermal energy in resistor Emf source does positive work to bring charge back to positive terminal. If circuit has a current I, what is rate of work done by emf source? P = dw = dq dt dt V emf = V emf I P must be equal to rate of energy dissipation in resistor: P diss = VI = I 2 R

Question 32.14 Lightbulbs Two lightbulbs operate at 120 V, but one has a power rating of 25 W while the other has a power rating of 100 W. Which one has the greater resistance? 1) the 25 W bulb 2) the 100 W bulb 3) both have the same 4) this has nothing to do with resistance

CT 29.6 US Bulbs are rated for 120 V. European bulbs are designed for 240 V. If you buy a 100 W light bulb as a souvenir in Paris, and plug it in at home, what happens? A: Glows as usual, like a 100 W bulb should B: Bzzzt, it burns out, too much power C: Glows half as bright (powerful) as usual D: It glows 1/4 as bright as usual E: None of these/???

Example Extension cords are often made from 18-gauge copper wire (diameter 1.0 mm). An electric saw that draws 7.0 A is operated at the end of an 8.0 m long extension cord. Find the rate of Ohmic dissipation in the extension cord. (ρ copper =1.7 x 10-8 Ω m).

CT 29.9 Two identical resistors are wired in series (one behind the other). They are attached to a battery a current is flowing through the circuit. The current in the second resistor is the current in the first resistor A: Equal to B: Half C: Smaller than, but not necessarily half