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. VHg = ?

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. VD=?

Explanation / Answer

current required for the load = 2.5/4 = 0.625

current supplied by three mercury cells = (1.35*3)/(0.035*3 + 6.4) = 0.622 A

current supplied by three dry cells = 0.616

so current supplied by three dry cells is much less than what required for the load while that supplied by three nercury cells is approximately equal, so latter is preferred.

part A

current in the circuit = 2.5/4 = 0.625

terminal voltage VHg = 3*1.35 - 0.625*0.035 = 4.028 V

part B

current in the circuit = 2.5/4 = 0.625

terminal voltage VD = 3*1.5 - 0.625*0.3 = 4.3125 V

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