# Chapter 18 Electric Currents

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1 Chapter 18 Electric Currents 1

2 The Electric Battery Volta discovered that electricity could be created if dissimilar metals were connected by a conductive solution called an electrolyte. This is a simple electric cell. 2

3 Electric Current Electric current is the rate of flow of charge through a conductor: (18-1) Unit of electric current: the ampere, A. 1 A = 1 C/s. 3

4 A complete circuit is one where current can flow all the way around. Note that the schematic drawing doesn t look much like the physical circuit! 4

5 In order for current to flow, there must be a path from one battery terminal, through the circuit, and back to the other battery terminal. Only one of these circuits will work: 5

6 By convention, current is defined as flowing from + to -. Electrons actually flow in the opposite direction, but not all currents consist of electrons. 6

7 Ohm s Law: Resistance and Resistors Experimentally, it is found that the current in a wire is proportional to the potential difference between its ends: 7

8 The ratio of voltage to current is called the resistance: (18-2a) (18-2b) 8

9 In many conductors, the resistance is independent of the voltage; this relationship is called Ohm s law. Materials that do not follow Ohm s law are called nonohmic. Unit of resistance: the ohm, Ω. 1 Ω = 1 V/A. 9

10 Resistivity The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area: (18-3) The constant ρ, the resistivity, is characteristic of the material. 10

11 Resistivity 11

12 Electric Power Power, as in kinematics, is the energy transformed by a device per unit time: (18-5) 12

13 The unit of power is the watt, W. For ohmic devices, we can make the substitutions: (18-6a) (18-6b) 13

14 What you pay for on your electric bill is not power, but energy the power consumption multiplied by the time. We have been measuring energy in joules, but the electric company measures it in kilowatthours, kwh. 14

15 Electrical Conduction in the Human Nervous System The human nervous system depends on the flow of electric charge. The basic elements of the nervous system are cells called neurons. Neurons have a main cell body, small attachments called dendrites, and a long tail called the axon. 15

16 Signals are received by the dendrites, propagated along the axon, and transmitted through a connection called a synapse. 16

17 This process depends on there being a dipole layer of charge on the cell membrane, and different concentrations of ions inside and outside the cell. 17

18 This applies to most cells in the body. Neurons can respond to a stimulus and conduct an electrical signal. This signal is in the form of an action potential. 18

19 The action potential propagates along the axon membrane. 19

20 Chapter 19 DC Circuits 20

21 EMF and Terminal Voltage Electric circuit needs battery or generator to produce current these are called sources of emf. Battery is a nearly constant voltage source, but does have a small internal resistance, which reduces the actual voltage from the ideal emf: (19-1) 21

22 This resistance behaves as though it were in series with the emf. 22

23 Resistors in Series and in Parallel A series connection has a single path from the battery, through each circuit element in turn, then back to the battery. 23

24 The current through each resistor is the same; the voltage depends on the resistance. The sum of the voltage drops across the resistors equals the battery voltage. (19-2) 24

25 From this we get the equivalent resistance (that single resistance that gives the same current in the circuit). (19-3) 25

26 A parallel connection splits the current; the voltage across each resistor is the same: 26

27 The total current is the sum of the currents across each resistor: 27

28 This gives the reciprocal of the equivalent resistance: (19-4) 28

29 Kirchhoff s Rules Some circuits cannot be broken down into series and parallel connections. 29

30 Kirchhoff s Rules For these circuits we use Kirchhoff s rules. Junction rule: The sum of currents entering a junction equals the sum of the currents leaving it. 30

31 Loop rule: The sum of the changes in potential around a closed loop is zero. 31

32 Problem Solving: Kirchhoff s Rules 1. Label each current. 2. Identify unknowns. 3. Apply junction and loop rules; you will need as many independent equations as there are unknowns. 4. Solve the equations, being careful with signs. 32

33 Circuits Containing Capacitors in Series and in Parallel Capacitors in parallel have the same voltage across each one: 33

34 In this case, the total capacitance is the sum: (19-5) 34

35 Capacitors in series have the same charge: 35

36 In this case, the reciprocals of the capacitances add to give the reciprocal of the equivalent capacitance: (19-6) 36

37 A Few Examples Resistor Network Kirchoff Circuit Capacitance Network 37

38 NEXT TIME EXAM #1 38

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