15. 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 σ. 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.