Engineering 1333: Electrical Circuits Topic 2 Power & Energy (Section 1.6)

9/8/2005Power and Energy 2 Sample Problem v + - i the current entering the element is given by Calculate the total charge in microCoulombs entering the device at terminal 1 By definition so Solution Since this is in coulombs the answer is 4000 µC

9/8/2005Power and Energy 3 Power p = power in watts w = energy in joules t = time in seconds By the chain rule Which means that

9/8/2005Power and Energy v + - i 2 1 v - + i v + i 2 1 v - + i Power absorbed by ckt Power delivered by ckt

9/8/2005Power and Energy 5 Batteries Single cell produces about 1.5 volts Think of it as being 1.5 volts “high” 1.5 V It stores charge internally, usually chemically We can make bigger cells, that store more charge, (or little ones that store less) But we can’t make the cells any higher Although different cell technologies have somewhat different heights

9/8/2005Power and Energy 6 Cell Technologies ChemistryV1V1 ChargeableComments Carbon-Zinc1.5nocheap Alkaline1.5noflashlights Mercury1.35nowatches, calculators Lead-Acid2.0yescars Ni-Cad1.2yespower tools Nickel-Metal- Hydride 1.2yeslaptops 1. Fully charged

9/8/2005Power and Energy 7 To make a battery we stack cells up Making a higher and higher voltage “hill” Three lead-acid cells makes a 6 volt battery And 6 gives us a car battery 6 v 12v

9/8/2005Power and Energy 8 Electricity vs Gravity Battery holds charge (capacity) Battery has a “height” (voltage) Battery stores energy Water tower holds mass (volume) Water tower has a height Water tower stores energy

9/8/2005Power and Energy 9 Hooking a Battery to a Heater The battery voltage appears across the heater Current flows from the battery into the heater From the battery’s point of view From the heater’s point of view It produces power It absorbs power v + - i battery heater

9/8/2005Power and Energy 10 Sample Problem v + - i Calculate the total energy in joules delivered to the element Solution Given So Integrating… So & Voltage was in Kv & Given By definition

9/8/2005Power and Energy 11 Problem 1.27 Elemen t VoltageCurrent a b c d e f30060 g h Direc tion 1 1 Power Absorbed