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Chapter 19 Electric Currents Electric Currents

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

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Electric Current Whenever electric charges of like signs move, an electric current is said to exist 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 current is the rate at which the charge flows through the wire The SI unit of current is Ampere (A) The SI unit of current is Ampere (A) 1 A = 1 C/s1 A = 1 C/s

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Example In a tv tube, 5 x 10 14 electrons shoot out in 4 s. What is the electric current?

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

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

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Resistance, cont Units of resistance are ohms (Ω) Units of resistance are ohms (Ω) 1 Ω = 1 V / A1 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 Resistance in a circuit arises due to collisions between the electrons carrying the current with the fixed atoms inside the conductor

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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 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 This statement has become known as Ohm’s Law V = I RV = I R Ohm’s Law is an empirical relationship that is valid only for certain materials Ohm’s Law is an empirical relationship that is valid only for certain materials Materials that obey Ohm’s Law are said to be ohmicMaterials that obey Ohm’s Law are said to be ohmic

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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?

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

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Parallel connection Series connection R1R1 R2R2 R3R3 R1R1 R2R2 R3R3 R eq = R 1 + R 2 + R 3 1/R eq = 1/R 1 +1/R 2 +1/R 3

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

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

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RaRa RbRb (1) 1/R eq = 1/R a + 1/R b (2) R eq is smaller than R a and R b 20 25 R eq ≈ 10 1000 = 1k 2 R eq < 2 Practically all the current flows Though the bottom one!!

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

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To be able to specify absolute potential at a given point, we need to specify a reference point “0” potential. GROUND R 1 = 6 6 V = “0” Then, at is +6 V.

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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 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 amountThe 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 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 increaseThe temperature of the resistor will increase

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

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Electrical Energy and Power, final The SI unit of power is Watt (W) The SI unit of power is Watt (W) I must be in Amperes, R in ohms and V in VoltsI must be in Amperes, R in ohms and V in Volts The unit of energy used by electric companies is the kilowatt-hour 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 suppliedThis is defined in terms of the unit of power and the amount of time it is supplied 1 kWh = 3.60 x 10 6 J1 kWh = 3.60 x 10 6 J

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

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

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

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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?

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

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

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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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