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Putting electrons in motion Electron movement through conductors Resistivity and Resistance – Ohm’s Law Electrical Power Current is the flow rate of charges through a surface area. The direction of the current is the direction of the flow of positive charges. Q I av t dQ I (t ) dt (C/s=Amperes) Q ( nV ) q Q ( nAx ) q Q ( nAvd t ) q Q I av nqvd A t vd : Drift Velocity A = 3.31 x 10-6 m2 I = 10 A Cu = 8.92 g/cm3 Q nqvd A I av t 10 A nvd 1.6 10 19 3.3110 6 V m = 63.5 g/mol NA = 6.02 x 1023 at/mol 1 electron per Cu atom m 63.5 7.12cm3 / mol 8.92 N A 6.02 10 23 8.46 10 22 el / cm3 8.46 10 28 el / m 3 n V 7.12 10 4 vd 2 . 23 10 m/s 19 6 28 1.6 10 3.31 10 8.46 10 Current Density: I J nqvd A J nqv d (for a uniform current perpendicular to the cross-section) General vector definition In some materials, the field applied and the current density are proportional. Ohm’s Law: J E Most metals obey Ohm’s Law : conductivity V El R Metal l l I A J l V A I Semiconductor diode (V/A = ) Resistivity is the inverse of conductivity. Both are intrinsic properties of the material. Resistance is a also a function of the shape and size of the device. 1 l R A Material (.m) Copper 1.7x10-8 Gold 2.44x10-8 Aluminum 2.82x10-8 Silicon 640 Rubber ~1013 A=2x10-4 m2 Al = 2.82x10-8 .m 10 cm RAl Al Glass = 3x1010 .m l 2.82 10 8 A RGlass Glass 0.1 5 1 . 41 10 4 2 10 l 0.1 13 1 . 5 10 3 1010 4 A 2 10 b R ln 2L a C L b 2ke ln a Atoms Electrons A regular array of atoms surrounded by a “cloud” of free electrons Random movement under zero field Random movement modified by a field F qE mea qE a me J E qE t v f v i at v i me Now take the average over all times. Then vi = 0 (random movement), v f vd nq 2 E J nqvd me qE qE t me me , where is the mean time between collisions nq 2 me me 2 nq l vd is the mean free path Resistivity in metals is linear with temperature over a limited range 0 1 T T0 R R0 1 T T0 : temperature coefficient of resistivity 1 0 T (C-1) U battery QV I U resistor (heat ) U battery + - V R U QV IV Electrical Power t t V.A = Watts(W) P IV V R 2 Symbol of a Resistor P I 2 R Power Dissipated on a Resistor Ia=Ib Ic=Id Ie=If Ia=Ic+Ie P60W > P30W Ic>Ie Ia=Ib> Ic=Id>Ie=If Current is the net rate of charge flow. Electrons move at the drift velocity. Resistance is the ratio of voltage applied to current. The ratio is linear for most metals. Resistivity is a material property. Electrical energy will be converted to thermal energy on a resistor. The rate of conversion is the power. Reading Assignment Chapter 28 – Direct Current Circuits WebAssign: Assignment 5