Battery-powered electricity is very expensive compared with that available from

Question

Battery-powered electricity is very expensive compared with that available from a wall receptacle.

Part A

Estimate the cost per kWh of an alkaline D-cell (cost $1.70). This battery can provide a continuous current of 24 mA for 860 h at 1.2 V .

Express your answer using two significant figures.

? $/kWh

Part B

Estimate the cost per kWh of an alkaline AA-cell (cost $1.25). This battery can provide a continuous current of 24 mA for 130 h at 1.2 V .

Express your answer using two significant figures.

Cost/kWh= ? $/kWh

Part C

Compare to normal 120-V ac house current at$0.10/kWh.

Express your answer using two significant figures.

Cost_Dcell / Cost_ac house current= ?

Part D

Express your answer using two significant figures.

Cost_AAcell / Cost_ac house current= ?

? $/kWh

Explanation / Answer

Part A :

P = i X V

P = 24 X 10-3 X 1.2

P = 0.0288 W

energy E = P t

E = 0.0288 X 860

E = 24.768 Wh

E = 2.4768 X 10-2 kWh

the cost is 1.70 / 2.4768 X 10-2= $ 68.63

Part B :

P i V

P = 24 X 10-3 X 1.2

P = 0.0288 W

E = 0.0288 X 130

E = 3.744 W h

= 3.744 X 10-3 k Wh

the cost = 1.25 / 3.744 X 10-3= $ 333.86

Part C :

for part A 686.3 times more expensive than the wall

for part B 3338.6 times more expensive than the wall

Part D :

Cost_AAcell / Cost_ac house current = $ 333.86 / $ 0.10

Cost_AAcell / Cost_ac house current = 3338.6

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