The starter circuit of an automobile drives the engine to turn over using power

Question

The starter circuit of an automobile drives the engine to turn over using power from the battery. Even a small amount of corrosion at the battery terminal can have a significant impact. The battery circuit is shown in figure (a). The battery provides and emf of 12.5 V emf with a 0.02 ohm internal resistance. It is attached a starter motor of resistance Rs = 0.15 ohm. Suppose that over time corrosion on the battery terminals and cables introduces an extra series resistance of just Rc = 0.10 ohm. as shown in figure (b). Set P0 as the power delivered to the starter in the absence of corrosion, and set P as the power delivered to the starter in the presence of corrosion. Determine the ratio P/P0. Express your answer using two significant figures.

Explanation / Answer

Po = I2R ,

now, total resistance in series = 0.02 + 0.15 ohms = 0.17 ohms

now, current , 12.5 /0.17 = 73.52 A

so power of starter =Po= I2 R = (73.52 A )2 * 0.15= 810.77 W

now,

when there is a corrosion current ,

net resistance = 0.02 + 0.15 ohms + 0.10 = 0.27 ohms

so current I = 12.5/0.27 ohms

=46.29 A

so, power = P = (46.29 A)2 * 0.15 = 321.5 W

so, ratio , = P/Po = 0.3965

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