Q66P - Fundamentals Of Physics

Question

The headlights of a moving car require about 10 A from the 12 V alternator, which is driven by the engine. Assume the alternator is efficient (its output electrical power is 80% of its input mechanical power), and calculate the horsepower the engine must supply to run the lights.

Step-by-Step Solution

Answer

The horsepower that the engine must supply to run the lights is 0.20hp . 

Step 1: The given data

1. Current required by the moving car’s headlights, i = 10A
2. Voltage required by the headlights, V = 12 V
3. The efficiency of the alternator, $P_{out}=0.80P_{in}$ 

Step 2: Understanding the concept of the power

By using the relations between power, potential, and current, we calculate the power watts. Using the relationship between Watts and Horsepower, we can convert this into horsepower.

Formulae:

The power required to be generated by the engine, P = iV                   (i)

The value of one horsepower to watt, 1hp=746 W                                (ii)

Step 3: Calculation of the horsepower to be supplied by the engine

From the initial condition from the problem, we have the value of the power as follows:

${\mathrm{P}}_{\mathrm{in}}=\frac{1}{0.80}{\mathrm{P}}_{\mathrm{out}}...................\left(\mathrm{a}\right)$

Now, using equation (i) and the given data, we can get the value of the output power as follows:

$$\begin{gathered} {\mathrm{P}}_{\mathrm{out}}=10\times 12 \\ =120\mathrm{W} \end{gathered}$$

Now, the value of the horsepower required by the engine can be calculated by using the above value in equation (a) as follows:

$$\begin{gathered} {\mathrm{P}}_{\mathrm{in}}=\frac{1}{0.80\times 746}\times 120 \\ =0.20\mathrm{hp} \end{gathered}$$

Hence, the value of the power is 0.20hp .