0195136047.pdf

2.8 PRACTICAL APPLICATION: A CASE STUDY 93

Black wire of jumper cable

Weak-battery car

Red wire of jumper cable

+

+

−

−

11 V

υg 1

− +

13 V

Figure 2.8.1Jumper cable connections for jump starting a car with a weak battery.

vg 1 − 13 + 11 =0orvg 1 =2V

wherevg 1 is the voltage across the airgap, or the voltage existing between the black jumper cable
and the negative terminal of the weak battery.
Now suppose one makes, by mistake, incorrect connections, as shown in Figure 2.8.2. Note
that the red jumper cable is connected between the positive terminal of the strong battery and the
negative terminal of the weak battery. Application of the KVL now fields

vg 2 − 13 − 11 =0orvg 2 =24 V

wherevg 2 is the gap voltage with incorrect connections. With such a large voltage difference,
when one tries to complete the black jumper cable connection, it presents a danger to both batteries
and to the person making the connections.

Energy to Start an Engine

A simplified circuit model for an automotive starter circuit is shown in Figure 2.8.3. Let the car
battery voltage be 12.5 V and let the automobile starter motor draw 60 A when turning over the
engine. If the engine starts after 10 seconds, we can easily calculate the power to the starter motor,
which is the same as the power out of the battery,

P=VI= 12. 5 × 60 =750 W

The energy required to start the engine can be computed as

W= 750 × 10 =7500 J

Thus, simple circuit models can be used to simulate various physical phenomena of practical
interest. They can then be analyzed by circuit-analysis techniques to yield meaningful solutions
rather easily.

Black wire of jumper cable

Weak-battery car

Red wire of jumper cable

+−

−

11 V

υg 2

− +

13 V

Figure 2.8.2Incorrect connections for jump starting a car with a weak battery.