The heat developed in an electric wire varies jointly as the wires resistance, the time the current flows, & the square of the current.

Question

The heat developed in an electric wire varies jointly as the wires resistance, the time the current flows, & the square of the current. In two minutes a current of 5 amps develops 1,200 heat units in a wire with a current of 10 amps in 5 minutes?

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Calantha 2 months 2021-07-29T17:37:07+00:00 1 Answers 2 views 0

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    2021-07-29T17:38:08+00:00

    Answer:

    4 ohms

    Step-by-step explanation:

    The question is “In two minutes a current of 5 amps develops 1,200 heat units in a wire of 8 ohms resistance. What resistance does a similar wire have, which develops 6,000 heat units with a current of 10 amps in 5 minutes?”

    Current, I₁ = 5 A

    Heat, Q₁ = 1200 units

    Resistance, R₁ = 8 ohms

    Time, t₁ = 2 min = 120 s

    New heat, Q₂ = 6000 units

    Current, I₂ = 10 A

    New time, t₂ = 5 min = 300 s

    We need to find the new resistance.

    Heat developed is given by :

    Q=I^2Rt

    \dfrac{Q_1}{I_1^2R_1t_1}=\dfrac{Q_2}{I_2^2R_2t_2}\\\\R_2=\dfrac{Q_2\times I_1^2R_1t_1}{Q_1I_2^2t_2}\\\\R_2=\dfrac{6000\times 5^2\times 8\times 120}{1200\times 10^2\times 300}\\\\=4\ \Omega

    So, the new resistance is 4 ohms.

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