1 CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCE BASIC CONCEPTS CURRENT and CURRENT DENSITY RESISTANCE and RESISTIVITY BATTERY INTERNAL RESISTANCE ENERGY AND POWER IN CIRCUITS 2 CURRENT IS THE MOVEMENT OF CHARGE IN A MATERIAL In some cases the objects that are moving are positive. 3 In other cases, for example in metals, the objects are negative (electrons). 4 Current is the time rate of passage of the charge. 5 Consider that there are n moving charged particles per volume And The average drift velocity is vd Then in time dt The particles move a distance of vddt In the volume, Avddt, shown in the figure there will be nAvddt particles. Each particle has a charge q. Thus in time dt the charge, dQ, that will pass through the cylinder is 6 ௗ Current is ௗொௗ௧ௗ Current density (current per unit cross‐section of the conductor) is ௗ Note that current density is a vector ௗ 7 RESISTIVITY Resistivity, ρ, is a characteristic of a material. 8 RESISTIVITY Resistivity, ρ, changes with temperature. ଴ ଴ Where ଴ is the value at 200 C. 9 For a metal: 10 For Semiconductor: 11 Some materials loose all resistivity – Superconductors: Discovered in 1911 by H. Kammerlingh Onnes. 12 RESISTANCE Resistance is a characteristic of an object. Resistance, R, is related to Resistivity, ρ, by 13 The longer the object the higher the resistance. The larger the cross‐section the smaller the resistance. If ρ is constant the total current through a conductor is proportional to the voltage across it. Or 14 The constant of proportionality is the resistance, R. Or This is Ohm’s Law. If a resistor obeys Ohm’s Law it is an Ohmic resistor. 15 Obeys Ohm’s Law: 16 Semiconductors are not Ohmic: 17 POWER DISIPATED WITH CURRENT FLOW. Remember q V Change in energy 18 And ௗ௤ௗ௧ Therefore Use Ohm’s Law 19 Or ௏ோ ଶଶ20 CALCULATE RESISTANCE A copper rod with cross section A has a length L what is its resistance? Work for ି଺ ଶ and . From Table 25.1 ି଼ Therefore ି଼ି଺ ଶ ିଶ 21 More difficult: Example 25.4 A cylinder with resistivity ρ has length L, inner radius a and outer radius b. Calculate the resistance for current flow from the inner to the outer walls. 22 Where is the path length of the current flow. And is the cross‐section for current flow. Now Consider a thin shell within the cylinder wall with radius , thickness and length . The area of the shell is . The path the current flows is . 23 Then Integrate to get . ௕௔ோୀ௕ோୀ௔ ௕௔௔௕ 24 CIRCUITS Circuit elements: 25 Other symbols will be added after we discuss magnetism. Internal Resistance Two points: If no current is in a circuit element there is no potential drop across the element. Batteries have internal resistance. 26 The figure is of a 12 V battery with no current in the circuit. The voltmeter will read 12 V. But if there is current: 27 The voltmeter will read less than 12 V. What is the current in the circuit? 28 What will the voltmeter read? ௥௘௔ௗ ௜௡௧௘௥௡௔௟ ௥௘௔ௗ ௥௘௔ௗ