A battery has an emf ε and internal resistance r. A variable load resistor R is connected across the terminals of the battery.
(a) Determine the value of R such that the potential difference across the terminals is a maximum.
(b) Determine the value of R so that the current in the circuit is a maximum.
(c) Determine the value of R so that the power delivered to the load resistor is a maximum.
Choosing the load resistance for maximum power transfer is a case of what is called impedance matching in general. Impedance matching is important in shifting gears on a bicycle, in connecting a loudspeaker to an audio amplifier, in connecting a battery charger to a bank of solar photoelectric cells, and in many other applications.
