An automotive battery has an emf of 10.6 V. When supplying power to the starter

Question

An automotive battery has an emf of 10.6 V. When supplying power to the starter motor, the current in the battery is 20.0 A, and the terminal voltage of the battery is 9.10V. (a) How much power is delivered by the battery due to the chemical reactions within the battery when the current in the battery is 20 A? kw (b) How much of this power is delivered to the starter when the current in the battery is 20 A ? kw (c) By how much does the chemical energy of the battery decrease if the current in the starter is 20 A for 7.1 s? kJ (d) How much energy is dissipated in the battery during those 7.1 seconds? J

Explanation / Answer

emf = 10.6 V ; I = 20 A ; V = 9.1 V

a)The power delivered by the battery due to chemical reactions will be:

P = I (emf)

P = 20 x 10.6 = 212 W

Hence, P = 212 W

b)This power will be:

P = VI

P = 9.1 x 20 = 182 W

Hence, P = 182 W

c)t = 7.1 s

we know from the defination of power

P = E/t => E = P x t

So the energy decrease will be:

E = 212 x 7.1 = 1505.2 J

Hence, E = 1505.2 J

d)E = P t

E = I^2 R t = I^2 (emf - V)/I t

E = 20 (10.6 - 9.1) x 7.1 = 213 W

Hence, E = 213 W

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