Batteries are rated in terms of ampere-hours (A·h). For example, a battery that can produce a current of 2.00 A for 3.00 h is rated at 6.00 A·h. (a) What is the total energy sto…

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asked Sep 6, 2020 134k views

1 Answer

Teetotum · Answer 1 · 2020-09-13T16:47:56+0000

(a) 423 J

The power of the battery is the ratio between the total energy stored (E) and the time elapsed (t):

P=(E)/(t)

However, the power is also the product of the voltage (V) and the current (I):

P=VI

Linking the two equations together,

$(E)/(t)=VI\\E=VIt$

Since we know:

V = 9.0 V

$I \cdot t = 47.0 A\cdot h$

We can calculate the total energy:

$E=(9.0 V)(47 A \cdot h)=423 J$

(b)
$7.79\cdot 10^(-6)$ dollars

The battery has a total energy of E = 423 J. (2)

1 Watt (W) is equal to 1 Joule (J) per second (s):

1 W = (1 J)/(1 s)

so 1 kW corresponds to 1000 J/s:

1 kW = (1000 J)/(1 s)

Multiplying both side by 1 hour (1 h):

$1 kW \cdot h = (1000 J)/(1 s) 1 h$

and
1 h = 3600 s , so

$1 kWh = (1000 J)/(1 s)\cdot 3600 s =3.6\cdot 10^6 J$

So we find the conversion between kWh and Joules. So now we can convert the energy from Joules (2) into kWh:

$1 kWh = 3.6\cdot 10^6 J = x : 423 J\\x=(1 kWh \cdot 423 J)/(3.6\cdot 10^6 J)=1.18\cdot 10^(-4)kWh$

And since the cost is $0.0660 per kilowatt-hour, the total cost will be

$C=$0.0660\cdot 1.18\cdot 10^(-4) kWh=7.79\cdot 10^(-6)$ dollars