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 stored in a 9.0 v battery rated at 47.0 a·h?

(b) at $0.0660 per kilowatt-hour, what is the value of the electricity produced by this battery? note: enter your response with hundredths precision.

(a) 423 J

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

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

Linking the two equations together,

Since we know:

V = 9.0 V

We can calculate the total energy:

(b) dollars

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

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

so 1 kW corresponds to 1000 J/s:

Multiplying both side by 1 hour (1 h):

and , so

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

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

dollars

two charges are fixed in place on the x-axis as shown. the charge at x = 0 is negative and has magnitude q = 2 μcoulombs (1 μcoulomb = 10-6 coulombs). the charge at x = d, (d = +12 cm), is positive and has magnitude q = 4 μcoulombs. find a point x = xo along the x-axis at which the electric field is zero.