The internal resistance of a 1.35-V mercury cell is 0.035 , whereas that of a 1.

Question

The internal resistance of a 1.35-V mercury cell is

0.035 , whereas that of a 1.5-V dry cell is 0.30 . Explain why three mercury cells can more effectively power a 2.5-W hearing aid that requires 4.0V than can three dry cells.

Part A: Find the terminal voltage across the series combinations of three batteries for mercury cells. Assume that the current in the battery is determined by the power and the required voltage. V= 3.98 V correct

Part B:

Find the terminal voltage across the series combinations of three batteries for dry cells. Assume that the current in the battery is determined by the power and the required voltage. V= 4.3125 V incorrect ?

Explanation / Answer

We can obtain the current drawn by the hearing aid from P = V I , where P = 2.5 W and V = 4.0 V ,

which gives I = 0.625 A .

The resistance of the hearing aid is R = V/I = 4.0/0.625 = 6.4 ohm.

For the mercury cells:

Em = 3 × 1.35 = 4.05 V and

For the dry cells:

Ed = 3 × 1.5 = 4.5 V and

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