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?
I need to know why this makes sense or not.
power = V i = V( V/R) = V^2/R sure enough
to triple the power at the same V, use 1/3 the resistance R
This can be done easily and very understandably by running three of the original Rs in parallel, like turning three stove burners on instead of one.
To triple the amount of heat generated by a stove element, we need to analyze the relationships stated in the problem.
The problem states that the heat generated by the stove element varies directly as the square of the voltage and inversely as the resistance. Mathematically, we can express this relationship as:
Heat ∝ Voltage^2 / Resistance
Given that the voltage remains constant, let's call it V. Therefore, the equation can be simplified to:
Heat ∝ V^2 / Resistance
To triple the amount of heat, we need to find a relationship where the new heat (let's call it Heat') is three times the original heat (Heat).
Heat' = 3 * Heat
Substituting the expression for heat in terms of voltage and resistance, we have:
V^2 / Resistance' = 3 * (V^2 / Resistance)
Now, since the voltage remains constant, the relationship between voltage and heat stays constant. Therefore, to triple the heat generated, we need to change the resistance.
From the equation above, we can solve for Resistance' (the new resistance):
Resistance' = Resistance / 3
So, to triple the amount of heat generated, the resistance needs to be reduced to one-third of its original value.
In conclusion, it makes sense that reducing the resistance by one-third would triple the heat generated since the heat generated by the stove element varies inversely with resistance. By decreasing the resistance, the element will experience less opposition to the flow of the electric current, resulting in an increase in heat output.