Question

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.

Name: Problem 76, Chapter 24: Essential University Physics Global Edition
Uploaded: 2020-05-15T01:17:39-08:00
Duration: 1 min 8 s
Channel: Mrinal Rana
Description: 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.

   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.

Essential University Physics Global Edition

Richard Wolfson 4th Edition

Chapter 24, Problem 76

Instant Answer

Solved by Expert Mrinal Rana

05/15/2020

Step 1

During a brownout, the voltage supplied to the conductor decreases. Since the resistance is nearly independent of temperature, we can assume that R remains constant. Using Ohm's Law, V = I * R, we can see that if the voltage (V) decreases and the resistance (R) Show more…

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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.

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Key Concepts

Resistive Power Dissipation

This concept refers to the calculation of power in a resistor using the formula P = V²/R. It shows that for a resistor with constant resistance, the power dissipated depends directly on the square of the applied voltage.

Voltage-Power Relationship

Because power is proportional to the square of voltage, a small decrease in voltage causes a larger percentage decrease in power dissipated. For instance, a 10% drop in voltage results in power falling to about 81% of its original value, which is approximately a 19% reduction.

Temperature Independence of Resistance

In scenarios where a conductor's resistance does not change significantly with temperature, the resistance remains effectively constant. This makes it possible to directly apply the squared relationship between voltage and power without needing to consider temperature-induced variations in resistance.

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