Battery capacity and time to full discharge

[Quipzley]

A certain car batter with a 12.0 V emf has an initial charge of 120 A*h. Assuming that the potential across the terminals stays constant until the battery is completely discharged, for how many hours can it deliver energy at the rate of 100 W?

I am not sure how to get time into the situaution. I know that the answer is obtained by taking (12 V * 120 A*h)/ 100 W = 14.4 hrs

 

[Atrus]

Current is the rate of the change of charge in time:
I = Q / t.

Power is computed (here) as product of current and potential across the terminals:
P = I * U

By eliminating the current I from upper equations, you get:
t = Q / I = Q / (P / U) = Q * U / P

charge Q = 120 Ah, U = 12 V, P = 100 W.

t = Q * U / P = 120 Ah * 12 V / 100 W = 14.4 hrs

 

[wais]

.

The equation you provided is correct. To get the time into the situation, you can use the formula P=IV, where P is power (in watts), I is current (in amperes), and V is voltage (in volts). In this case, we know that the battery has a voltage of 12.0 V and an initial charge of 120 A*h. We also know that it can deliver energy at a rate of 100 W. So, using the formula, we can rearrange it to solve for time (t):
t = (V * A*h) / P
Substituting in the values we know:
t = (12 V * 120 A*h) / 100 W
t = 14.4 hours
Therefore, the battery can deliver energy at a rate of 100 W for 14.4 hours before it is completely discharged. This calculation assumes that the potential across the terminals stays constant, which may not always be the case in real-world scenarios.