The performance of the starter circuit in a an automobile can be significantly d

Question

The performance of the starter circuit in a an automobile can be significantly degraded by a small amount of corrosion on a battery terminal. Figure 26-38a depicts a properly functioning circuit with a battery (12.5-V emf, 0,02 ohms internal resistance) attached via corrosion-free cables to a starter motor of resistance R_s = 0.15 ohms. Suppose that later, corrosion between a battery terminal and a starter cable introduces an extra series resistance of just R_c = 0.10 ohms into the circuit as suggested in figure. Let P_0 be the power delivered to the starter in the circuit free of corrosion, and let P be the power delivered to the circuit with corrosion. Determine P/P_0.

FIGURE IS IN THE BOOK.

Explanation / Answer

Given emf   = 12.5 V       internal resistance   r = 0.02        resistance R s = 0.15                         R c   = 0.1     current through the circuit free of corrision is              I = / R + r                   = 12.5 / ( 0.15 +0.02 )                   = 73.5294 A     power delivered to the starter in the circuit free of corrosion,               P = I 2 R                   = ( 73.5294 ) 2 ( 0.15 )                    = 810.986 W corrosion between a battery terminal and a starter cable introduces an extra series resistance of just R_c                R = Rc + R s                   = 0.1+0.15 = 0.25    current through the circuit with corrision is               I = / R + r                 =   12.5 / ( 0.25 +0.02)                 = 46.2962 A   power delivered to the starter in the circuit with corrosion               Po =I 2 R                   = ( 46.2962) 2 ( 0.25 )                    = 535.836W P / Po   = 810.986   / 535.836                = 1.5134    

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