A voltmeter is used to measure the voltage of voltage

Chapter , Problem 15

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A voltmeter is used to measure the voltage of voltage sources, such as batteries. Every time this device is used, a random error is made, independent of other measurements, with mean 0 and standard deviation . Suppose that we want to measure the voltages, V1 and V2, of two batteries. If a measurement with smaller error variance is preferable, determine which of the following methods should be used: (a) To measure V1 and V2 separately. (b) To measure V = V1 + V2 and W = V1 V2, and then find V1 and V2 from V1 = (V + W )/2 and V2 = (V W )/2. There are methods available for engineers to do these. For example, to measure V1 + V2, they attach batteries in series so that each battery pushes current in the same direction. To measure V1 V2, they attach the batteries in series so that they push current in opposite directions. Assume that the internal resistances of the batteries are negligible.