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Unit 3 Day 2: Resistivity, Power & AC Current • Resistivity and its Temperature Dependence • Electric Power • Heat Generation in Electric Circuits • AC Current • Average power Resistivity • Resistance R, of a wire is proportional to its length, and inversely proportional to its crosssectional area: L resistivity m R A Resistivity • Resistivity is a material property • The reciprocal of resistivity is conductivity 1 conductivity m 1 • Resistivity is temperature dependent T 0 1 T T0 T resistivit y at temp 0 resistivit y at 20 C T0 20 C (room temp) temp coefficient of resistivit y C 1 Electric Power • Electric Power delivered to the load is: P dU dQ V dt dt or P I V or P I 2 R 2 V or P R by substituting V I R V by substituting I R • SI: Watts (W) 1W = 1 Volt-Amp Electric Power • Energy purchased from the power company to use to power our home is: P dt watt sec • We purchase energy in large quantities, so it is more convenient to use units of: kw hr kilowatt hours 1kw hr 1000W 3600s 3.6 10 J 6 Electric Power • When power is delivered to a load, the current thru the wires generate heat (thermal energy) • The power is dissipated in the load as heat because of the resistance of the load 2 PI R • Too much current in a wire or a load will cause it to overheat and may cause fire. Preventing Circuit Overheating • Lower resistance in the wires by using low resistivity material (ie: Cu or Al), use large diameter wires, and keeping wire lengths as short as possible. L R A • Use current protection devices such as fuses or circuit breakers. Circuit Breakers • Circuit breakers (CB)use a bi-metallic strip to open the circuit Household Circuit Management • Connection of too many household appliances to one circuit will cause a CB to trip • If this circuit is protected with a 20A CB, it will trip to prevent overheating of the wires and prevent fire P 3450W I 28.75 A V 120V • Extension cords can be a dangerous fire hazard, if they are rated at 10A or less. Alternating Current • DC Current is constant with time. I0 • AC Current varies periodically with time I I 0 sin t , 2f V V0 sin t V V0 I sin t R R AC Power P I 2 R I 02 R sin( t ) or P P0 sin( t ) where P0 Peak Power P Average Power • Since the current is squared, power is always positive RMS Values • It is difficult to measure peak or average AC Voltage & Current. Therefore a convenient unit of measure was developed called the rms values. • rms is an abbreviation for root-mean-square value • To find the rms value, take the square root of mean value of the squared term. V0 2 2 1 Vrms V 2 V0 .707V0 2 I rms I 2 1 2 I0 I .707 I 0 2 2 0 Average Power P Vrms I rms V0 I 0 V0 I 0 P0 2 2 2 2 2 P 12 I 02 R I rms R or 2 2 V V P 12 0 rms R R