The electric starter in an automobile equipped with a 12 V battery draws a current of 100.00 A when in operation. Suppose it takes the motor 4.00 s to start the engine. What amount of electric energy has been withdrawn from the battery?

Answer:
(in J) 4.80×103 J

The automobile is equipped with a generator that delivers 5.90 A to the battery when the engine is running. How long must the engine run in order for the generator to restore the energy in the battery to its original level?

Need help with the second question.. not sure how to relate the two.

12 V * 5.9 amps * time in seconds = 4.8*10^3

To solve the second question, you need to relate the electric energy withdrawn from the battery (found in the first question) to the energy supplied by the generator.

First, let's calculate the electric energy withdrawn from the battery. We know that the current drawn is 100.00 A and the time taken is 4.00 s.

The formula for calculating electric energy is given by:
Energy = Power x Time

Since we have the current (I) and the time (t), we can calculate the power (P).

Power = Current x Voltage

Given that the voltage is 12 V, we can calculate the power:
Power = 100.00 A x 12 V = 1200 W

Now, we can calculate the electric energy withdrawn:
Energy = Power x Time = 1200 W x 4.00 s = 4800 J

Therefore, the amount of electric energy withdrawn from the battery is 4.80 × 10^3 J.

Now, to find the time required for the generator to restore the energy in the battery, we can use the formula:

Time = Energy / Power

Given that the current supplied by the generator is 5.90 A, and the power is 12 V x 5.90 A = 70.80 W (using Power = Current x Voltage), we can substitute these values into the formula:

Time = (4.80 × 10^3 J) / (70.80 W)

Calculating this gives:
Time = 67.9 seconds

Therefore, the engine must run for approximately 67.9 seconds for the generator to restore the energy in the battery to its original level.

To answer the second question, we can use the concept of electrical energy and relate it to the current and time.

Recall that electric energy is given by the formula:

Energy = Power × Time

where Power is the rate at which energy is drawn or supplied. In this case, since the generator is supplying energy to the battery, the power is positive.

We can calculate the power supplied by the generator using the formula:

Power = Current × Voltage

In this case, the current supplied by the generator is 5.90 A. We know the battery voltage is 12 V. Therefore, the power supplied by the generator is:

Power = 5.90 A × 12 V = 70.8 W

Now, we need to find the amount of electric energy that needs to be restored to the battery. We already found that it was 4.80 × 10^3 J (as provided in the answer to the first question).

Using the formula for energy again, we can rearrange it to solve for time:

Time = Energy / Power

Plugging in the values:

Time = (4.80 × 10^3 J) / (70.8 W)

Calculating this:

Time ≈ 67.8 s

Therefore, the engine must run for approximately 67.8 seconds in order for the generator to restore the energy in the battery to its original level.