Answer to Question 05/99
CIRCUIT OF BATTERIESThe question was:
Twelve identical 1 volt batteries are connected into an electrical circuit
as shown in the figure. What will the voltmeter show?
(5/99) The problem has been solved by Eitan Federovsky (e-mail eitan@peach-networks.com), by Andy Tan (e-mail andytan@cyberway.com.sg), physics tutor at the National Junior College, Singapore, and his colleagues, and by D. Augier (e-mail augier@irsamc2.ups-tlse.fr).
The answer: The voltmeter will show zero voltage.
The solution:
Assuming that the voltmeter has infinite resistance, the current in the loop will be equal to the total electromotive force, 12 volts, divided by the total resistance, 12 times the internal resistance R of one battery. So the current will be (1 V)/R. The internal voltage drop in each battery (current times internal resistance) will therefore equal R (1 V)/R=1 V which is the electromotive force on that battery. The voltage drop across a single battery will be equal to the difference between the electromotive force and the internal voltage drop and therefore it will be equal to zero. The same is true for any group of batteries.
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