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April 24, 2006 Science A52 – Section #8: Electricity: Electrical energy (batteries, wall sockets, etc.) is derived from the movement of electric charges (usually electrons). Ohm’s Law: Voltage = Current * Resistance V=I*R Power: Power = Voltage * Current # Watts = V * I Resistance: Resistivity is the inverse of the conductivity of a material. Copper has a very high conductivity – thus a low resistivity. Your body has a low conductivity, and thus a high resistivity. Resistance is given by: R L A R = resistance {units = ohms - } = resistivity {units = ohms*length} L =length A =area of wire Table 2: Resistivities of select metals from The Physics Hypertextbook. Metal Resistivity (nΩ*m) Copper 17.1 Silver 15.9 Aluminum 26.5 Example 1: What is the resistance of a 1 km long copper wire with a radius of 0.1 cm? The resistance of a wire is given by L where ( m) is the resistivity and depends on the material of the wire, L A (m) is the length of the wire and A (m2) the cross-sectional area. R For copper the resistivity is 17.1n m 17.1109 m The cross-section area is A r 2 0.1cm 0.1102 m 3.14 106 m 2 The resistance of the wire R 2 2 L A 17.110 9 m 10 3 m 3.14 106 m 2 5.4 Example 2: Voltage and current What is the current in the wire if you apply a 110 V voltage? The current and the voltage are related through the resistance. I V 110V 20.4 Amps R 5.4 Example 3: Power losses What are the power losses in the wire? The power losses are calculated from the current and resistance. P I 2 R 20.4 Amps 5.4 2241W 2 Magnetism: Magnetic fields originate from the movement of electric charges. This relationship is quantified in the Biot-Savart equation. The magnetic field surrounding a long straight current carrying wire is given by: o I 2 r B =magnetic field {Teslas – use right hand rule for direction} o =4 *10-7 I=current {Amps} R=radius {meters} B This idea is used to make electro-magnets by coiling wire along a ferrous metal (like iron) and running current through the wire. Example: A toaster oven uses 1500 watts and plugs into a 120V outlet. Calculate the magnitude and direction of the magnetic field 1m from the cord. I P / V 1500W /120V 12.5 Amps B o I 4 *107 *12.5 Amps 2.5*106 Tesla 2 r 2 *1m Transformers: Induction of magnetic fields back to current allows one to build a transformer to raise or lower AC voltage (think of the large plastic socket on your cell phone charger). d m dt d m V2 N 2 dt V V2 N 2 ( 1 ) N1 V1 N 1 V2 ( N2 )V1 N1 Example: Your Cell Phone battery is 12V, and you want to build a transformer to plug into a wall socket at 120V. If you have a 150 turns around a ferrous core on the side connected to your phone, how many turns must you have on the socket side? V 120V N wall wall N phone 150turns 1,500turns V 12V phone Semiconductors: Transistors can be thought of as a voltage regulated valve that controls the flow of electrons (i.e. current). Below is a simple diagram: The height of ΔE can be modified with an applied voltage ( higher V, lower ΔE, more current flows). If an electron has more energy than ΔE than it will flow from the emitter to collector. Below is a plot of the logarithm of current vs. voltage.