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Current and Resistance 1 12-11-2014 FCI

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Define the current. Understand the microscopic description of current. Discuss the rat at which the power transfer to a device in an electric current. 212-11-2014FCI

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2-1 Electric current 2-2 Resistance and Ohm’s Law 2-3 Current density, conductivity and resistivity 2-4 Electrical Energy and Power 312-11-2014FCI

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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 412-11-2014FCI

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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 through the atoms 512-11-2014FCI

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For most metals, resistivity increases approximately linearly with temperature over a limited temperature range ◦ ρ is the resistivity at some temperature T ◦ ρ o is the resistivity at some reference temperature T o T o is usually taken to be 20° C is the temperature coefficient of resistivity 612-11-2014FCI

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Since the resistance of a conductor with uniform cross sectional area is proportional to the resistivity, you can find the effect of temperature on resistance 712-11-2014FCI

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A class of materials and compounds whose resistances fall to virtually zero below a certain temperature, T C ◦ T C is called the critical temperature The graph is the same as a normal metal above T C, but suddenly drops to zero at T C 12-11-20149FCI

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In a circuit, as a charge moves through the battery, the electrical potential energy of the system is increased by ΔQΔV 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 1012-11-2014FCI

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Consider the circuit shown Imagine a quantity of positive charge, Q, moving around the circuit from point A back to point A 1112-11-2014FCI

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Point A is the reference point ◦ It is grounded and its potential is taken to be zero As the charge moves through the battery from A to B, the potential energy of the system increases by Q V ◦ The chemical energy of the battery decreases by the same amount 1212-11-2014FCI

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As the charge moves through the resistor, from C to D, it loses energy in collisions with the atoms of the resistor The energy is transferred to internal energy 13 When the charge returns to A, the net result is that some chemical energy of the battery has been delivered to the resistor and caused its temperature to rise 12-11-2014FCI

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The rate at which the energy is lost is the power From Ohm’s Law, alternate forms of power are 1412-11-2014FCI

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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 10 6 J 1512-11-2014FCI

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The same potential difference is applied to the two lightbulbs shown in Figure.Which one of the following statements is true? (a) The 30-W bulb carries the greater current and has the higher resistance. (b) The 30-W bulb carries the greater current, but the 60-W bulb has the higher resistance. 1612-11-2014FCI

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(c) The 30-W bulb has the higher resistance, but the 60-W bulb carries the greater current. (d) The 60-W bulb carries the greater current and has the higher resistance. 1712-11-2014FCI

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(c). Because the potential difference ∆V is the same across the two bulbs and because the power delivered to a conductor is P= I V, the 60-W bulb, with its higher power rating, must carry the greater current. The 30-W bulb has the higher resistance because it draws less current at the same potential difference. 1812-11-2014FCI

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2012-11-2014FCI

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1. The electric current “I “ in a conductor is defined as where dQ is the charge that passes through a cross section of the conductor in a time interval dt. The SI unit of current is the ampere (A), where 1 A = 1 C/s. The average current in a conductor is related to the motion of the charge carriers through the relationship 21 where n is the density of charge carriers, q is the charge on each carrier, v d is the drift speed, and A is the cross- sectional area of the conductor. 12-11-2014FCI

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2. The current density in an ohmic conductor is proportional to the electric field according to the expression 22 The proportionality constant σ is called the conductivity of the material of which the conductor is made. The inverse of & is known as resistivity ρ (that is, ρ = 1/ σ). The last equation is known as Ohm’s law, and a material is said to obey this law if the ratio of its current density J to its applied electric field E is a constant that is independent of the applied field. 12-11-2014FCI

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23 3. The resistance R of a conductor is defined as where ∆V is the potential difference across it, and I is the current it carries. The SI unit of resistance is volts per ampere, which is defined to be 1 ohm; that is, 1Ω = 1 V/A. If the resistance is independent of the applied potential difference, the conductor obeys Ohm’s law. 12-11-2014FCI

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4. If a potential difference ∆V is maintained across a circuit element, the power, or rate at which energy is supplied to the element, is 24 Because the potential difference across a resistor is given by ∆V = IR, we can express the power delivered to a resistor in the form The energy delivered to a resistor by electrical transmission appears in the form of internal energy in the resistor. 12-11-2014FCI

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1. The charge carriers in metals are A. electrons. B. positrons. C. protons. D. a mix of protons and electrons. 12-11-2014FCI25

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2. A battery is connected to a resistor. Increasing the resistance of the resistor will A. increase the current in the circuit. B. decrease the current in the circuit. C. not affect the current in the circuit. 12-11-2014FCI26

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3. A battery is connected to a resistor. As charge flows, the chemical energy of the battery is dissipated as A. current. B. voltage. C. charge. D. thermal energy 12-11-2014FCI27

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