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Chapter 18: Problem 70

During a "brownout," which occurs when the power companies cannot keep up with high demand, the voltage of the household circuits drops below its normal $120 \mathrm{V} .\( (a) If the voltage drops to \)108 \mathrm{V},$ what would be the power consumed by a "100-W" light-bulb (that is, a light-bulb that consumes \(100.0 \mathrm{W}\) when connected to \(120 \mathrm{V}\) )? Ignore (for now) changes in the resistance of the light-bulb filament. (b) More realistically, the light-bulb filament will not be as hot as usual during the brownout. Does this make the power drop more or less than that you calculated in part (a)? Explain.

Short Answer

Expert verified
Answer: The power consumption will be less than 81 W when considering the change in resistance due to filament temperature during the brownout.

Step by step solution

01

Calculate resistance of the light-bulb filament at normal voltage

We are given that the power consumed by the light-bulb is 100 W at 120 V. Using the formula P = V^2/R, we can determine the resistance of the light-bulb filament. 100 W = (120 V)^2 / R => R = (120 V)^2 / 100 W = 14400 / 100 = 144 惟
02

Calculate power consumed at 108 V

Now we need to calculate the power consumed by the light-bulb when the voltage drops to 108 V. Again, we can use the formula P = V^2/R to find the power consumed. P = (108 V)^2 / 144 惟 = 11664 / 144 = 81 W So the power consumed by the light-bulb during a brownout is 81 W.
03

Analyze the effect of filament temperature on resistance

In the second part, we need to consider the change in resistance due to the change in filament temperature. Typically, as the temperature of the filament increases, the resistance also increases. This means that if the light-bulb filament is not as hot as usual during the brownout (lower temperature), the resistance of the filament will decrease.
04

Discuss the effect on power consumption

If the resistance of the filament decreases due to a lower temperature during the brownout, the power consumed by the light-bulb would also decrease compared to the situation where we ignore the change in resistance (i.e., power consumption would be less than 81 W). Therefore, considering the change in resistance due to the temperature change, the power drop will be more than the one calculated in part (a).

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