Consider the following diagram, where V 1 = 14.5 V, V 2 = 9.5 V, R 1 = 71.0 m, a
ID: 1529668 • Letter: C
Question
Consider the following diagram, where V1 = 14.5 V, V2 = 9.5 V, R1 = 71.0 m, and R2 = 17.0 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 = 0.900 , find the current in each branch. (Take the positive direction to be up.)
What is the terminal voltage of the battery?
V
Is the battery charging or discharging?
chargingdischarging
IAlternator = A IBattery = A IResistor = A Altemator BatteryExplanation / Answer
Let us assume that the current in the loop 1 is I1 and in the loop 2 is I2.
Now we will write the equation by KVL
I1R1 -V1 + (I1 -I2)R2 +V2 = 0
.071I1 - 14.5+9.5 +(I1 -I2)0.017 = 0
0.088I1 - 0.017I2 = 5 ----------(1)
Now in loop 2
0.9I2 + (I2 - I1)0.017 -V2 = 0
0.917I2 - 0.017I1 = 9.5 ------------(2)
Solving 1 and 2
I1 = 59.03 A , I2 = 11.45 A
Now current in the alternator = I1 = 59.03 A
Current in the battery = I1 - I2 = 59.03 - 11.45 = 47.58 A
since the current direction is downward therefore it would be negative.
Current in the battery= -47.58 A
Current in the resistor R = I2 = -11.45 A