Question

An automobile battery, when connected to a car radio, provides 12.5 V to the radio. When connected to a set of headlights, it provides 11.7 V to the headlights. Assume the radio can be modeled as a 6.25Ω resistor and the headlights can be modeled as a 0.65Ω resistor. It is required to design and additional load to draw maximum power from the battery while connected along with the radio and the headlights.

Answer 1

When connected in series, a headlight and starter consume 56.52 W of power from a 12.0 V battery.

Step-by-step explanation:

When two resistors are connected in series, the total resistance is the sum of the individual resistances. In this case, the headlight has a resistance of 2.50 ohms and the starter has a resistance of 0.05 ohms.

To find the total resistance, we add the individual resistances: 2.50 ohms + 0.05 ohms = 2.55 ohms.

Now, we can use Ohm's law to calculate the total current flowing through the circuit. Ohm's law states that V = I * R, where V is the voltage, I is the current, and R is the resistance. Since the voltage is 12.0 V and the resistance is 2.55 ohms, we can rearrange the equation to solve for I: I = V / R. Plugging in the values, we get I = 12.0 V / 2.55 ohms = 4.71 A.

The power consumed by the circuit can be calculated using the formula P = I * V, where P is the power, I is the current, and V is the voltage. Plugging in the values, we get P = 4.71 A * 12.0 V = 56.52 W.

Answer 2

The maximum power required from a battery when connected to with radio and headlights is 235.6 W.

How to calculate the maximum power?

The maximum power required from a battery when connected to with radio and headlights is calculated as follows;

P = V²/r

where;

• V is the voltage supplied
• r is the resistance

The maximum power required from a battery when connected to with radio and headlights is calculated as;

P = (12.5²)/(6.25) + (11.7² ) / (0.65)

P = 25 W + 210.6 W

P = 235.6 W

Thus, the maximum power required from a battery when connected to with radio and headlights is 235.6 W.