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12 January, 00:16

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?

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  1. 12 January, 00:29
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    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.
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