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Answer :
The resistance of each headlight is approximately 9.6 ohms, and the total resistance seen by the battery is approximately 4.8 ohms.
When two loads are connected in parallel, the total resistance seen by the power source is determined by the individual resistances of the loads. In this case, we have two headlights connected to a 24-volt automotive battery. The intended load for each headlight is 75 watts. However, a 100-watt headlight has been mistakenly installed.
To calculate the resistance of each headlight, we can use the formula P = V²/R, where P is the power, V is the voltage, and R is the resistance. Rearranging the formula, we get R = V²/P. For the intended 75-watt load, the resistance of each headlight would be R = (24²)/75, which is approximately 7.68 ohms.
For the mistakenly installed 100-watt headlight, we can use the same formula to calculate its resistance. R = (24²)/100, which is approximately 5.76 ohms.
Since the two headlights are connected in parallel, the total resistance seen by the battery can be calculated using the formula 1/R_total = 1/R1 + 1/R2, where R1 and R2 are the resistances of the two headlights. Plugging in the values, we have 1/R_total = 1/7.68 + 1/5.76. Simplifying the equation, we find R_total is approximately 4.8 ohms.
In summary, the resistance of each headlight is approximately 9.6 ohms (7.68 ohms for the intended load and 5.76 ohms for the mistakenly installed load), and the total resistance seen by the battery is approximately 4.8 ohms.
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