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Chapter 24: Problem 68

A brownout occurs when an electric utility can't supply enough power to meet demand. Rather than cut off some customers completely, the utility reduces the voltage across its system. Brownouts are most likely on hot summer days, when heavy air-conditioning loads drive up demand for electricity. In a particular brownout, the utility reduces the voltage by \(10 \%.\) During the brownout, the power dissipated in conductors whose resistance is nearly independent of temperature a. decreases by approximately \(10 \%.\) b. decreases by approximately \(20 \%.\) c. decreases by approximately \(5 \%.\) d. You can't tell without knowing the resistance.

Short Answer

Expert verified
The power dissipated in conductors whose resistance is nearly independent of temperature decreases by approximately 19%, so the closest answer is (b) decreases by approximately 20%.

Step by step solution

01

Understand the variables and equations

Relate power (P), voltage (V) and resistance (R) using the formula P = V^2 / R, known as Power Formula derived from Ohm's law.
02

Calculate the power after the reduction in voltage

After the brownout, the voltage is reduced by 10%, which means the new voltage V_new = 0.9 * V. Substitute V_new in the power formula to get the new power: P_new = (0.9V)^2 / R = 0.81 * V^2 / R.
03

Calculate the power reduction percentage

The ratio of the new power to the original power is P_new / P = 0.81. This means the power has decreased by 1 - 0.81 = 0.19 or 19% approximately.

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Most popular questions from this chapter

A \(240-\mathrm{V}\) electric motor is \(90 \%\) efficient, meaning that \(90 \%\) of the energy supplied to it ends up as mechanical work. If the motor lifts a \(200-\mathrm{N}\) weight at \(3.1 \mathrm{m} / \mathrm{s}\), how much current does it draw?

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