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

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,$P_{out}=0.80P_{in}$

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)

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 .