Answer:
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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