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Chapter 19

Chapter 19. Electric Currents. Sources of Electromotive Force. Devices supply electrical energy, e.g. batteries, electric generators Two (or more) terminals with a potential difference. When charge flows out from one terminal, equal charge flows into the other terminal. Electric Current.

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Chapter 19

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  1. Chapter 19 Electric Currents

  2. Sources of Electromotive Force • Devices supply electrical energy, e.g. batteries, electric generators • Two (or more) terminals with a potential difference. • When charge flows out from one terminal, equal charge flows into the other terminal

  3. Electric Current • Whenever electric charges of like signs move, an electric current is said to exist • The current is the rate at which the charge flows through the wire • The SI unit of current is Ampere (A) • 1 A = 1 C/s

  4. Example In a tv tube, 5 x 1014 electrons shoot out in 4 s. What is the electric current?

  5. Ohm’s law e I Current: amount of charge flowing through a point per unit time Current flows from higher potential to lower potential I e e= R I R e

  6. Resistance • In a conductor, the voltage applied across the ends of the conductor is proportional to the current through the conductor • The constant of proportionality is the resistance of the conductor

  7. Resistance, cont • Units of resistance are ohms (Ω) • 1 Ω = 1 V / A • Resistance in a circuit arises due to collisions between the electrons carrying the current with the fixed atoms inside the conductor

  8. Ohm’s Law • Experiments show that for many materials, including most metals, the resistance remains constant over a wide range of applied voltages or currents • This statement has become known as Ohm’s Law • V = I R • Ohm’s Law is an empirical relationship that is valid only for certain materials • Materials that obey Ohm’s Law are said to be ohmic

  9. Example A 1.57 V battery connects to a light bulb. If the current through the bulb is 0.21 A, what is the resistance of the bulb?

  10. Req V = R I Resistance, R = V/I [R] = V/A = W (Ohm) For a fixed potential difference across a resistor, the larger R, the smaller current passing through it.

  11. Parallel connection Series connection R1 R2 R1 R3 R2 R3 Req = R1 + R2 + R3 1/Req = 1/R1+1/R2+1/R3

  12. Electrical wires can be bent and/or stretched. • A Node point (branching point) can be moved arbitrarily • along the wire.

  13. There are n identical resistors connected in parallel. Req? 1/Req = 1/R + 1/R + 1/R + … + 1/R = n/R Req = R/n

  14. Ra • (1) 1/Req = 1/Ra + 1/Rb • (2) Req is smaller than Ra and Rb Rb 1000 = 1k 20 2 25 Req < 2 Practically all the current flows Though the bottom one!! Req ≈ 10

  15. Ohm’s law:e = R·I R = 6 I = e/R = (6 V)/(6 Ohm) = 1.0 A 6 V What is the electric potential at ? We cannot tell the absolute potential at this point. If e at is +6 V, then 0 V at If e at is +3 V, then -3 V at For both, the potential diff. is 6 V.

  16. Then, e at is +6 V. To be able to specify absolutepotential at a given point, we need to specify a reference point “0” potential. GROUND R1 = 6 e = “0” 6 V

  17. Electrical Energy and Power • In a circuit, as a charge moves through the battery, the electrical potential energy of the system is increased by QV • The chemical potential energy of the battery decreases by the same amount • As the charge moves through a resistor, it loses this potential energy during collisions with atoms in the resistor • The temperature of the resistor will increase

  18. Electrical Energy and Power, cont • The rate at which the energy is lost is the power • From Ohm’s Law, alternate forms of power are

  19. Electrical Energy and Power, final • The SI unit of power is Watt (W) • I must be in Amperes, R in ohms and V in Volts • The unit of energy used by electric companies is the kilowatt-hour • This is defined in terms of the unit of power and the amount of time it is supplied • 1 kWh = 3.60 x 106 J

  20. Example • Light bulb 60 W, 120 V. Find resistance of the light bulb. • Bulbs in series • Bulbs in parallel

  21. Resistivity • The resistance of an ohmic conductor is proportional to its length, L, and inversely proportional to its cross-sectional area, A • ρ is the constant of proportionality and is called the resistivity of the material

  22. A L R = r L /A Resistivity: material parameter same for any shape in a given material. [r] = W.m e.g. for copper r = 1.7 x 10-8 gold r = 2.44 x 10-8 tungsten r = 5.6 x 10-8 iron r = 9.5 x 10-8 nickel-chrome r = 150 x 10-8

  23. Example A silver wire has a resistance of 2. What would be the resistance of a silver wire twice its length and half its diameter?

  24. Temperature Variation of Resistivity • For most metals, resistivity increases with increasing temperature • With a higher temperature, the metal’s constituent atoms vibrate with increasing amplitude • The electrons find it more difficult to pass the atoms

  25. Temperature Variation of Resistance, cont • For most metals, resistivity increases approximately linearly with temperature over a limited temperature range, resulting • T-To is temperature change •  is the temperature coefficient of resistivity • Ro is the resistance at To Ag: 3.8 x 10-3 /C Cu: 3.9 x 10-3 /C Fe:5.0 x 10-3 /C

  26. Example Light bulb (60 W; 120 V; 240 ) operates at 1800 C. What is the resistance of the filament (tungsten) at 20 C?

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