Question

A typical rechargeable deep-cycle battery for an electric trolling motor (fishing boat) delivers 10A of current at a voltage of 12V for 10 hours. (a) How much charge (in coulombs) flows through the battery in this interval? (The answer is a positive value.) (b) How much energy (in joules) does the battery deliver? (The answer is a positive value.) (c) How much energy (in watt-hours) does the battery deliver? (The answer is a positive value.)

Answer 1

The charge that flows through the battery in 10 hours is 100 coulombs. The battery delivers 1200 joules of energy. The battery delivers 0.33 watt-hours of energy.

Step-by-step explanation:

(a) To find the charge that flows through the battery in 10 hours, we can use the formula: charge = current x time. In this case, the current is 10A and the time is 10 hours, so the charge is 10A x 10 hours = 100 coulombs.

(b) The energy delivered by the battery can be calculated using the formula: energy = charge x voltage. Plugging in the values, we get energy = 100 coulombs x 12V = 1200 joules.

(c) To convert the energy to watt-hours, we divide the energy in joules by 3600 (since 1 watt-hour = 3600 joules). So the battery delivers 1200 joules / 3600 = 0.33 watt-hours.

Answer 2

a) 360 kQ

b) 4.32 MJ

c) 1200 W-h

Step-by-step explanation:

a) The definition of the current is.

`I= (Q)/(t)`

having a count that 10 hours = 36.000 s

`Q = I*t`

`Q = 36000*10 = 360.000 [Q]`

b) The definition of the Energy in power terms is.

`E = \int\limits^(t)_(0) {P} \, dt`

and the definition of power is:

`P = V*I = 12 * 10 = 120 [W]`

replacing in the energy formula.

`E = \int\limits^(36.000)_(0) {120} \, dt`

solving the integral, have into account that t is in seconds.

`E=P*t=120*36000=4.320.000=4.32 [MJ]`

c) The energy in W-h, we can find it multiplying power by hours

`E = P*t =120*10 = 1200 W-h`.