## PHYS345 Electricity and Electronics

Real Batteries and Battery Testers

 Previously we have been considering the power supply for a circuit to be a pure emf. Real batteries are better modeled as an emf in series with an internal resistance. The internal resistance r is included to account for power dissipation which is not recoverable within the battery when current is flowing. Since the internal resistance of the battery is in series with the load the equivalent resistance of the circuit is Req = R + r. The current is thus reduced owing to the internal resistance, i = emf / (r+R), from what it would be in its absense. The potential difference across the load, equivalent to that across the battery, is less than the full emf of the battery because of the voltage drop across the internal resistance. emf = iR + ir Vload = iR = emf - ir The so-called terminal voltage of a battery is lower than the emf when it is discharging because of the voltage drop across the internal resistance. If, on the other hand, the battery is being charged by an external source such as a recharger, the current will be forced through the battery in the opposite direction; the terminal voltage will then be higher than the emf by the amount of the voltage difference across its internal resistance. Battery Testers Thus if no current flows through a battery, its terminal voltage in that case will be identical to its emf. Good voltmeters have extremely high resistance; the input resistance of modern multimeters typically exceeds 10 megaohms (10 x 106 ohms). Thus the current flow in the circuit shown at the left will be much less than a microamp. Since the internal resistance of a fresh battery is typically one ohm or less, the voltage drop across the internal resistance will be insignificant when the terminal voltage is measured with a good voltmeter. To properly test the effects of internal resistance in a battery, a load must be added so that a current will flow through the battery. If no currents flow, no information about the internal resistance can be gotten. Ideally the load added will represent the conditions under which the battery will actually be used. After the load is added to the battery under test, the terminal voltage of the battery is measured with a voltmeter as shown at the left. Thus a battery tester is a voltmeter in parallel with a load resistor, both connected across the battery to be tested. Battery Aging One important failure mode of a battery is that the internal resistance r increases with age. Internal resistance of a battery may also increase dramatically if an attempt is made to extract the energy of the battery too quickly via large currents.

The table below shows measurements of the terminal voltage of two AA alkaline batteries, one new and one used, made with a voltmeter and with a battery tester with load resistance of 15.6 ohm.

Battery
condition
Measured
emf
Measured
terminal
voltage
Calculated
current
Voltage
across r
Calculated
internal
resistance
just
voltmeter
battery
tester
through

new 1.53 V 1.49 V 96 mA 0.04 V 0.4 ohm
old 1.25 V 1.00 V 64 mA 0.25 V 3.9 ohm

Other Online Battery Resources
 Fun and Learning: Battery Science:     Anatomy, Chemistry, Performance, and Inside a Battery Timeline and Quiz Comprehensive Battery Guide and Guide to Proper Battery Care Battery Buzz The Anatomy of the On-Battery Tester Life with and without Batteries Battery Know How, an ACDelco Training Program presented by the Automotive Parts & Accessories Association