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 12.5V emf with a 0.02 internal resistance. It is attached a starter motor of resistance RS=  0.20   . Suppose that over time corrosion on the battery terminals and cables introduces an extra series resistance of just RC=0.10, 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. P/P0 = ______________

Explanation / Answer

a) power to starter can be represented as I2Rs where I is the current in the curcult

now ,when there is no corrosion ,

net resistance in series = 0.02 + 0.2 = 0.22 ohms

current in circuit = 12.5 / 0.22 = 56.82 A

so , power P 0 = I2R = (56.82 A)2 * 0.2 = 645.70

now , when there is corrosion there is a net resistance = 0.02 +0.2 + 0.10 = 0.32 ohms

so, current = 12.5/0.32 A= 39.06 A

so , power (P ) = (39.06 A) 2 * 0.2 = 305.14

so , ratio= P/Po = 305.14 /645.70 = 0.473

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