A serries of energy questions having to do with total power, total energy sored and time of power.?

Question

A flashlight has 2 1.5 V D batteries arranged so that their voltages add together, with a 2-W bulb. These batteries are rated at 3.5 amp-hours each.

What is the total power that can be expeneded by the batteries? What is the total energy sotred in the flashlight batteries? How long can the flaishlight keep the bulb lit at its rated power of 2-W?

Answer 1

Let's walk through it:

From bulb power of P = U*I = 2 W and voltage U = 3 V you can find bulb resistance R = U/I = U/(P/U) = U^2/P = 9/2 = 4.5 ohm.
The current flowing through the bulb I = U/R = 3/4.5 = 2/3 = 0.67 A.

The total power spent is P = 2 W.
The total energy stored in the battery E = Q*U = 3.5*3 VAh = 10.5 VAh = 10.5*3600 VAs = 37800 J.
If the electric charge stored in the battery Q = 3.5 Ah then with the current 2/3 A the battery will last Q/I = 3.5/0.67 = 5.25 h and that's how long will the bulb lit.

Note: this is all under assumption that the internal battery resistance is zero.