CH 20-1

Surface Charge Gradient When a wire is connected to a battery, a surface charge gradient (i.e. variation) is “immediately” established on the outside of the wire. The surface charge (gradient) creates a uniform electric field on the inside of the wire that points from high potential to low potential along the wire. + − Low Potential High Potential

Poll For an electron at the point shown, what will be the direction of the force (due to the electric field created by surface charge) on the electron. + − Low Potential High Potential

Flow of electrons Moving charges collide with atoms and other electrons in a conductor. The electrons travel with a constant speed -- called drift speed. They lose potential energy as they travel through the wire (U = qV). Lost potential energy results in an increase in thermal energy and light.

Current Electron Current is the number of electrons that passes a cross section of the wire per second. + − Current is the charge that passes a cross section of the wire per second. Low Potential High Potential

Example If a current of 1 A flows in a wire, how many electrons pass a cross-section of the wire in 1 second?

Drift speed Current depends on charge density, area, and the drift speed.

Example What is the number density of conduction electrons in copper? Copper has a density of 8900 kg/m3, an atomic mass of 63.5 g/mol, and 1 free electron per atom.

Example What is the drift speed of electrons in a copper wire of diameter 1 mm if the current is 1 A.

Resistance More collisions will mean that fewer electrons pass a cross section of wire per second. This property of the wire is called resistance. For a higher resistance of the wire, less current flows through the wire when it is connected to a battery. Units of R is the ohm 

+ − Ohm’s Law For a wire (or an “ideal resistor”) For a given potential difference, current and resistance are inversely proportional. High Potential

Example You connect a 1.5 V battery to a 6  light bulb. What will be the current through the filament of the bulb?

Resistance of a wire Resistance of a wire depends on the collisions that an electron makes as it travels through the wire. Three factors thus affect resistance: resistivity (which depends on the particular metal), the length of the wire, and the area of the wire.

Resistivity

Analyzing simple circuits Treat resistors and light bulbs as “ideal resistors” even though light bulbs certainly have a resistance that certainly changes with temperature. Assume that all other wires are “ideal wires.”

Poll A 1.5 V battery is connected to Bulb A and you observe its brightness. You then replace the bulb with Bulb B and observe that it is brighter. Through which bulb is the current the greatest? Bulb A Bulb B Neither, because the current is the same through each bulb.

Poll A 1.5 V battery is connected to Bulb A and you observe its brightness. You then replace the bulb with Bulb B and observe that it is brighter. Across which bulb is the potential difference the greatest? Bulb A Bulb B Neither, because the current is the same through each bulb.

Poll A 1.5 V battery is connected to Bulb A and you observe its brightness. You then replace the bulb with Bulb B and observe that it is brighter. Which bulb has a greater resistance? Bulb A Bulb B Neither, because the current is the same through each bulb.

Poll Suppose that Filament #1 has the same length as Filament #2 and they are made of the same material. But Filament #2 has a greater cross-sectional area. Which filament has a greater resistance? Filament #1 Filament #2 Neither, because the filaments have the same resistance.

Poll Suppose that Filament #1 has the same length as Filament #2 and they are made of the same material. But Filament #2 has a greater cross-sectional area. Which filament will be brighter in a light bulb that is connected to a battery? Filament #1 Filament #2 Neither, because the filaments have the same resistance.

Poll Suppose that Filament #1 has the same cross-sectional area as Filament #2 and they are made of the same material. But Filament #2 has a greater length. Which filament will have a greater resistance? Filament #1 Filament #2 Neither, because the filaments have the same resistance.

Poll Suppose that Filament #1 has the same area as Filament #2 and they are made of the same material. But Filament #2 has a greater length. If in a bulb and connected to a battery, which filament will be brighter? Filament #1 Filament #2 Neither, because the filaments have the same resistance.