Question

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

Answer 1

resistance must quadruple

Explanation:

You want to know the change in resistance required to quadruple the amount of heat if heat is proportional to the square of voltage, inversely proportional to resistance, and the voltage is quadrupled.

Resistance

Let H represent the heat generated for voltage V and resistance R. We want to find R, the new resistance required, when V is replaced by 4V, and H is replaced by 4H.

H = V²/R

4H = (4V)²/R'

4(V²/R) = 16V²/R'

R' = (16/4)R . . . . . . . multiply by RR'/(4V²)

R' = 4R

The resistance must quadruple if the amount of heat is to be quadrupled.

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