Consider the following diagram, where V 1 = 13.0 V, V 2 = 9.5 V, R 1 = 72.0 m ?

Question

Consider the following diagram, where V1 = 13.0 V, V2 = 9.5 V, R1 = 72.0 m?, and R2 = 14.0 m?.

The figure shows a simplified circuit diagram for an automobile. The equivalent resistor R represents the total electrical load due to spark plugs, lights, radio, fans, starter, rear window defroster, and the like in parallel. If R = 0.800 ?, find the current in each branch. (Take the positive direction to be up.)

IAlternator =      A IBattery =      A IResistor =      A Consider the following diagram, where V1 = 13.0 V, V2 = 9.5 V, R1 = 72.0 m?, and R2 = 14.0 m?. The figure shows a simplified circuit diagram for an automobile. The equivalent resistor R represents the total electrical load due to spark plugs, lights, radio, fans, starter, rear window defroster, and the like in parallel. If R = 0.800 ?, find the current in each branch. (Take the positive direction to be up.) What is the terminal voltage of the battery?

Explanation / Answer

Ir = Ib + Ia

voltatage drop across battery = voltage drop across alternator = voltage drop acroos resistor

=> V2 - R2*Ib = V1 - R1*Ia = Ir*R

=> 9.5 - 0.014*Ib = 13 - .072*Ia = Ir*0.8

putting Ir = Ib + Ia and simplifying with first two eqaution respectively we get

9.5 = 0.8Ia + 0.786Ib

13 = 0.8Ib + 0.728Ia

solving Ia = -38.61 amp ;Ib= 51.39 amp

hence Ir = 12.78 amp

terminal voltage of battery = 13 - 0.72 =12.28 V

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