Jumper cables are connected from a fresh battery in one car to charge a dead bat

Question

Jumper cables are connected from a fresh battery in one car to charge a dead battery in another car. The figure below shows the circuit diagram for this situation. While the cables are connected, the ignition switch of the car with the dead battery is closed and the starter is activated to start the engine. (Let R = 1.40 Ohm and Rs = 0.09 Ohm.) Determine the current in the starter A downward Determine the current in the dead battery. A upward Is the dead battery being charged while the starter is operating?

Explanation / Answer

a) Let I1 and I2 are upward currents in middle and left part of circuit respectively. and I3 downward from Rs.

I1 + I2 = I3 ................... (1)

12 - 0.01I2 + 1.4 I1 -12 = 0 =====> I1 = 0.007 I2 .................... (2)

12 - 1.4 I1 - 0.09 I3 = 0 ======== > I1 + 0.064 I3 = 8.57 ........... (3)

Put (2) into (1) and (3), we get

0.007 I2 + I2 = I3 ====> 1.007 I2 = I3

and 0.007 I2 + 0.064 I3 = 8.57

  0.007 I2 + 0.064(1.007 I2) = 8.57 ====> I2 = 119.95 A

b) I1 = 0.007 I2 = 0.007*119.95 = 0.83965 A (in dead battery)

I3 = I1 + I2 = 0.83965 + 119.95 = 120.8 A (in the starter)

c) No

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