Aaa, aa, … d batteries have an open circuit voltage (emf) of 1.5 v. the differencebetween different sizes is in their lifetime (total energy storage). a aaa battery has alife of about 0.5 a-hr while a d battery has a life of about 10 a-hr. of course thesenumbers depend on how quickly you discharge them and on the manufacturer, but thesenumbers are roughly correct. one important difference between batteries is their internalresistance – alkaline (now the standard) d cells are about 0.1ω .suppose that you have a multi-speed winch that is 50% efficient (50% of energy useddoes useful work) run off a d cell, and that you are trying to lift a mass of 60 kg (hmmm, i wonder what mass that would be). the winch acts as load with a variable resistance rlthat is speed dependent. a) suppose the winch is set to super-slow speed. then the load (winch motor) resistanceis much greater than the battery’s internal resistance and you can assume that there isno loss of energy to internal resistance. how high can the winch lift the mass beforedischarging the battery? b) to what resistance rl should the winch be set in order to have the battery lift themass at the fastest rate? what is this fastest rate (m/sec)? hint: you want tomaximize the power delivery to the winch (power dissipated by rl).c) at this fastest lift rate how high can the winch lift the mass before discharging thebattery? d) compare the cost of powering a desk light with d cells as opposed to plugging it intothe wall. does it make sense to use rechargeable batteries? residential electricity costs
about $0.1/kwh.