The heat generated by a stove element varies directly as the square of the voltage and inversely...

Question:

The heat generated by a stove element varies directly as the square of the voltage and inversely as the resistance. If the voltage remains constant, what needs to be done to triple the amount of heat generated?

Inverse Proportion:

Inverse proportion means that when one variable increases the other variable decreases. This is not the same as a negative slope but it is the product of the two variables is a constant. Thus, in the equation {eq}a = \dfrac 1 c {/eq}, when {eq}c {/eq} decreases, the value of {eq}a {/eq} increases.

Answer and Explanation:

An expression of the equation being described in the given where heat, {eq}Q {/eq}, is generated that varies diectly as the square of the voltage, {eq}V {/eq}, and inversely as the resistance, {eq}R {/eq}, would be:

{eq}Q=\dfrac {V^2}{R} {/eq}

Since the voltage is constant, if the heat is to be tripled it means that the resistance has to change. Specifically, the resistance has to be divided by three such that:

{eq}Q = \dfrac {V^2}{\dfrac R 3} \\ Q = V^2 \times \dfrac 3 R \\ Q = 3 \dfrac {V^2}{R} {/eq}

Thus, dividing the resistance by three will triple the heat generated.


Learn more about this topic:

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Inversely Proportional: Definition, Formula & Examples

from High School Precalculus: Tutoring Solution

Chapter 20 / Lesson 12
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