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

Answer:

increase the resistance by 8.333333333

Step-by-step explanation:

Q ∝ V2 / R  (I hope you can see it - it is a teeny-tiny little proportionality symbol)

so if we increase V by a factor of 5

Q ∝ (5V)2 / R

we need to find what factor of increase or decrease will give a 3x increase in heat (Q)

3Q = (5V)2 / ?•R

but we do not need to concern ourselves with the variables, just with the factors

3 = 52 / ?  (lets replace the ? with a variable 'x' to be more algebraic

3 = 52 / x

x = 52 / 3 = 25 / 3 = 8.33

and to check ourselves

Q = (5V)2 / 8.33•R = 25•V2 / 8.33•R = 3•(V2/R)  √check

So increase the resistance by 8.333333333