You get home and your Roku remote isn’t working correctly, so you install new batteries. However, this doesn’t fix the problem. The equivalent circuit for a AAA battery is shown to the right. A healthy AAA battery will have more than 1.3V and less than 300m\Omega internal resistance.
You take the batteries out and a simple battery tester reports that one of the batteries is “bad”, but the other one shows “good”. You replace the bad battery, with a new battery that reads “good” on your tester, but the remote still doesn’t work.
A. (5 pts) Your EE roommate comes home and says that the battery tester you were using only measures the voltage, and doesn’t apply any load to test them. They pull out a voltmeter and the batteries measure 1.17V, 1.35V, and 1.6V, respectively, but your roommate says that this still isn’t enough to determine whether all three are good. Explain.
B. (5 pts) Your roommate rigs up some alligator clips and a small light bulb to test the batteries. The light bulb is rated for 4W at 8V. What is the bulb resistance?
C. (5 pts) Explain why this light bulb is not a reasonable load to apply to test the batteries’ internal resistances.
D. (5 pts) Correcting your dumb EE roommate, you change the bulb out for a 1\Omega resistor like the small 0.25-Watt ones we have in the lab in your parts box. The 1.6V battery measures 0.4V with the resistor attached. Find the internal resistance, and determine whether the battery is actually healthy.
E. (5 pts) You hook up the 1.35V battery to the resistor and burn your fingers on the resistor. Why did this happen? Hint: Suppose the battery is healthy...how much power would you be burning up in the resistor?