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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.)

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joshuaandresblanco

Answer:

a) 360 kQ

b) 4.32 MJ

c) 1200 W-h

Explanation:

a) The definition of the current is.

[tex]I= \frac{Q}{t}[/tex]

having a count that 10 hours = 36.000 s

[tex]Q = I*t[/tex]

[tex] Q = 36000*10 = 360.000 [Q] [/tex]

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

[tex]E = \int\limits^{t}_{0} {P} \, dt[/tex]

and the definition of power is:

[tex] P = V*I = 12 * 10 = 120 [W][/tex]

replacing in the energy formula.

[tex]E = \int\limits^{36.000}_{0} {120} \, dt[/tex]

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

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

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

[tex] E = P*t =120*10 = 1200 W-h [/tex].

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