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1. Electric Currents

   AP Physics B Chapter 18 Notes
2. Electric Current and Circuits An electric circuit consists of an energy source and an energy consuming device, connected by wires through which electric charges move. The schematic on the right represents the picture.
3. Electric Current and Circuits In order for current to flow in a circuit, there must be complete path from one terminal of a battery, through the circuit, and back to the other terminal of the battery.
4. Electric Battery Batteries are often used to provide the energy source. Volta discovered that electricity could be created if dissimilar metals were connected by a conducting electrolyte. A chemical reaction occurs to transfer electrons from one terminal to another.
5. Electric Battery and EMF The chemical reaction maintains a potential difference across the terminals, whether current flows or not. The maximum potential difference is called electromotive force (emf)
6. Electric Current and Charge Flow The electric current is the amount of charge per unit time that flows through a surface perpendicular to the direction of motion of the charges. Units: Ampere A= C/s
7. Electric Current Example The current in a 3V pocket calculator is 0.17mA . In one hour of operation a) how much charge flows in the circuit and b) how much energy does the battery deliver?
8. Ohm’s Law and Resistors Experimentally it was found that current flowing in a wire is proportional to the voltage across the circuit:
9. Ohm’s Law and Resistors The resistance, R, is defined as the ratio of voltage to current: or Units: ohm (Ω) = V/A
10. Ohm’s Law and Resistors Ohm’s Law says the resistance of a metal conductor is independent of the voltage. This is true for certain materials only, nonohmic materials behave as in (b). So it is not a true law.
11. Ohm’s Law and Resistors Resistance, R, represents to what extent the current can flow freely in the circuit, i.e. the larger R, the more the electrons scatter with atoms in the material. These scatterings slow down electrons and transfer energy as heat to the material. To the extent that a wire or an electrical device offers resistance to electrical flow, it is called a resistor.
12. Ohm’s Law Example P 7, pg. 515 An electric clothes dryer has a heating element with a resistance of 9.6Ω. a) What is the current in the element when it is connected to 240V? b) How much charge passes through the element in 50 min?
13. Current Summary Some helpful clarifications: Batteries maintain (nearly) constant V; current varies Resistance is a property of material or device used, not voltage. Current has a direction but is not a vector. Current/charge does not get used up; whatever goes in comes out.
14. Resistivity For a wide range of materials, the resistance R of apieceof material of length L and cross-sectional area A is: Where ρis resistivity, a property of the material and units are [Ω m] Intuitively this makes sense: For larger A  R decreases For larger L  R increases L A ρ
15. Resistivity and Temperature Resistivity for any given material varies with temperature: or, using  As your book discusses, if the temperature of some materials is lowered below some critical temperature, TC, they become Superconductors and ρ = 0, i.e. they have no resistance to current flow. Resistivity at temperature T0 Temperature coefficient of resistivity
16. Resistivity
17. Resistivity Example The instructions for an electric lawn mower suggest that a 20-gauge extension cord can be used for distances up to 35 m, but a thicker 16-gauge cord should be used for longer distances. The cross sectional area of a 20-gauge wire is 5.2x10-7m2, while that of a 16-gauge wire is 13x10-7 m2. Determine the resistance of (a) 35 m of 20-gauge copper wire and (b) 75 m of 16-gauge copper wire. The resistivity of Cu is 1.68 x 10-8Ωm.
18. Power Power, as in kinematics, is the rate of energy transfer by a device per unit time: But remember definition of I, so: P= IV Using Ohm’s Law we can also write: Units are Watts and W=J/s
19. Power and PG&E We consume energy, not power, so PG&E bills us for energy (Joules essentially). One Joule is a relatively small amount of energy, and since W=J/s, we are billed in kWh. One kWh= 3.6 x106 J. Utility capacity is measured in power units (MW).
20. Power A couple of notes on using the power equations: P=IV can be used for any device (or to find power delivered to a circuit) P=I2R = V2/R can only be used for resistors (to find power dissipated by them—remember wires are resistors unless we are told to ignore)
21. Power—Examples P31 pg. 517 Find the resistance of a hair dryer at two settings: 850W and 1250W. Predict which is higher first! P 39 pg. 517 A power station delivers 625kW of power at12kV to a factory through wires with 3Ωof resistance. How much less power is wasted if the electricity is delivered at 50kV?
22. Power and Household Circuits Resistance in household wiring is relatively low, but if current is too high, the wire can become hot enough to melt insulation and start a fire. Circuit breakers are used to prevent this:
23. Alternating Current Current from a battery flows steadily in one direction (DC—graph a) Current from a power plant varies sinusoidally (AC—graph b)
24. Alternating Current As a result, voltage varies sinusoidally with time: So does current: where V0 and I0 are peak voltage and current
25. Alternating Current Using P = I2R we find: But we only get the average power over time:
26. Alternating Current Current and voltage have average values of zero, so we use the root mean square (rms) value: Reported values of V (e.g.,120V) are the rms values
27. Alternating Current--Example P 46 pg. 517 A 1800W arc welder is connected to a 660V ac line. Calculate a) the peak voltage and b) the peak current