Consider the following diagram, where V1 = 13.5 V, V2 = 11.0 V, R1 = 80.0 m, and

Question

Consider the following diagram, where V1 = 13.5 V, V2 = 11.0 V, R1 = 80.0 m, and R2 = 18.0 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 = 0.620 , find the current in each branch. (Take the positive direction to be up.)

I Alternator= ?

I Battery= ?

I Resistor= ?

(All answers have the unit A)

Explanation / Answer

Applying KVL in left side loop:

- i1 R1 + V1 - V2 - i2 R2 = 0

0.080i1 + 0.018 i2 = 2.5 .... (i)

KVL in right side loop:

i2 R2 + V2 - i R = 0

- 0.018i2 + 0.620i = 11 .... (ii)

Applying KCL,

i1 = i2 + i

i1 - i2 - i = 0 .... (iii)

Solving, i1 = 8965/311 up

i2 = 3350/311 down

i = 5615/311 down

I alternator =28.8 A

I Batery = - 10.8 A

I resistor = - 18.1 A

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