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Current, Resistance, and Electromotive Force Sections 1-5, 7 Chapter 28 1 Current Movement of charges Scalar quantity Amount of charge transferred per unit time Q I t 2 Measured in amperes or amps 1A = 1 C/s Traditional current direction 3 Current flows in the direction that positive charge would flow. It is impossible to experimentally determine which charges are moving. We know that the electrons are actually moving in the opposite direction of current flow, but we keep with tradition. Drift velocity 4 Speed of the moving particles. n particles per unit volume are moving in a conductor with speed v. In a time t, each particle moves vt. If the conductor has a cross sectional area A, then the number of particles in a given section during a given time interval is nAvt. Drift velocity If each particle has a charge q, the total charge moving through the volume in a given time interval is Q = nqvAt. Q I nqvA t 5 Current density Current per unit cross-sectional area I J nqv A 6 Resistivity Ratio of electric field to current density E J 7 Big resistivity means that a big E field is needed to cause a given current density, Or that a small E field will cause a small current density Resistivity For metals, increases with temperature. T 0 1 T T0 8 For semiconductors, it decreases with temperature. For superconductors it drops suddenly as temperature decreases. Resistance Related to resistivity. Often more useful, because it uses total current, not current density. It also uses potential difference instead of E field. Measured in ohms 1 W = 1 V/A R 9 l A Ohm’s Law Very important V IR 10 Temperature dependence RT R0 1 T T0 11 Resistors 12 Circuit elements designed to have a specific resistance. Used to control current. Circuits 13 We need a complete circuit to have a steady current. Charge moves in the direction of decreasing potential energy – like rolling downhill. We need to have a device to move the charge back uphill – like the pump in a fountain. Electromotive force 14 What makes the charge move from lower to higher potential. Abbreviated emf – say each letter. Batteries Solar cells Generators Circuits 15 Contain resistors, sources of emf, and possibly other circuit elements. The algebraic sum of the potential differences around the path is zero. In a simple loop, the current is the same everywhere. Sources of emf Maintain a constant potential difference, or voltage, regardless of the current flowing through them. Have positive and negative terminals. – The potential is higher at the positive terminal. E V 16 Internal resistance Real sources of emf have some internal resistance to current flow. So, V E Ir E Ir IR E I Rr 17 Example on page 632 18 Look at schematic drawings of circuits. Kirchoff’s loop rule The sum of the voltages around a loop is zero. Choose a current direction and draw it on the diagram. It’s OK if you’re wrong. – 19 If at the end we get negative current, then the direction was wrong. No big deal. Kirchoff’s loop rule 20 If we go across a battery from – to +, we add the voltage. + to – we subtract it. Always subtract IR from a resistor See example on page 635 Power Work done per unit time, measured in watts. 1 W is 1 J/s 1 A is 1 C/s 1 V is 1 J/C (1A)(1V) = 1 J/s P IV 21 Power Using Ohm’s law, V = IR P I IR PI R 2 22 V P V R 2 V P R Power output of emf source P IV IE I r 2 23 Power input of emf source P IV IE I r 2 24 Physiological effects of currents 25 Nervous system is electrical Currents as low as 1 mA can disrupt the nervous system enough to cause death by fibrillation. Larger currents through the heart may actually be safer – the heart is temporarily paralyzed and has a better chance of restarting with a normal heartbeat