The heat generated by a stove element varies directly as the square of the voltage and inversely as the resistance. If the voltage increases by a factor of 10 , what needs to be done to quadruple the amount of heat generated?

The resistance needs to be increased by a factor of 25 to quadruple the amount of heat generated

Explanation:

Let H be the heat generated by the stove element, V its voltage and R its resistance.

So, H ∝ V²/R

H = kV²/R

HR/V² = k

H₁R₁/V₁² = H₂R₂/V₂²

If H₂ = 4H₁ and V₂ = 10V₁

H₁R₁/V₁² = 4H₁R₂ / (10V₁) ²

H₁R₁/V₁² = 4H₁R₂/100V₁²

R₁ = R₂/25

R₂ = 25R₁

The resistance needs to be increased by a factor of 25 to quadruple the amount of heat generated.