Chapter 21, Problem 52P

Jumper cables are connected from a fresh battery in one car to charge a dead battery in another car. Figure P21.52 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. Determine the current in (a) the starter and (b) the dead battery. (c) Is the dead battery being charged while the starter is operating?

Figure P21.52

P21.52 Using Kirchhoff’s rules and suppressing units,

$12.0-(0.01)I_1-(0.06)I_3=0$    [1]

$12.0+(1.00)I_2-(0.06)I_3=0$    [2]

$\text{and }{I}_1=I_2+I_3.$    [3]

Substitute [3] into [1]:

$\begin{array}{l}12.0-(0.01)(I_2+I_3)-(0.06)I_3=0\\ 12.0-(0.01)I_2-(0.07)I_3=0\end{array}$    [4]

ANS. FIG. P21.52

Solving [4] and [2] simultaneously gives

1. (a) I₃ = 172 A = $\boxed{172\text{ A downward}}$ in the starter.
2. (b) I₂ = −1.70 A = $\boxed{1.70\text{ A upward}}$ in the dead battery.
3. (c) $\boxed{\begin{array}{l}\text{No},\text{ the current in the dead battery is upward in Figure }\\ \text{P21}\text{.52, so it is not being charged}\text{. The dead battery is }\\ \text{providing a small amount of power to operate the starter,}\\ \text{so it is not really }“\text{dead}\text{.}”\end{array}}$