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By Tony R. Kuphaldt
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Consider the use of a DC voltmeter in determining whether or not two DC voltage sources are aiding or opposing each other, assuming that both sources are unlabeled as to their polarities. Using the voltmeter to measure across the first source: 44 CHAPTER 2. COMPLEX NUMBERS The meter tells us +24 volts V A A V OFF A COM Source 1 Source 2 Total voltage? This first measurement of +24 across the left-hand voltage source tells us that the black lead of the meter really is touching the negative side of voltage source #1, and the red lead of the meter really is touching the positive.
Thus, we know that source #2 is a battery facing in the opposite direction: 24 V 17 V Source 1 Source 2 + Total voltage = 7 V It should be obvious to any experienced student of DC electricity that these two batteries are opposing one another. By definition, opposing voltages subtract from one another, so we subtract 17 volts from 24 volts to obtain the total voltage across the two: 7 volts. We could, however, draw the two sources as nondescript boxes, labeled with the exact voltage figures obtained by the voltmeter, the polarity marks indicating voltmeter test lead placement: 24 V - -17 V + Source 1 - + Source 2 According to this diagram, the polarity marks (which indicate meter test lead placement) indicate 46 CHAPTER 2.
This second voltmeter reading, however, is a negative (-) 17 volts, which tells us that the black test lead is actually touching the positive side of voltage source #2, while the red test lead is actually touching the negative. Thus, we know that source #2 is a battery facing in the opposite direction: 24 V 17 V Source 1 Source 2 + Total voltage = 7 V It should be obvious to any experienced student of DC electricity that these two batteries are opposing one another. By definition, opposing voltages subtract from one another, so we subtract 17 volts from 24 volts to obtain the total voltage across the two: 7 volts.