calculate the length of the resistor of a circular wire in a heater element connected to a 240V supply and the heater consumes 8 joules of energy in 0,25 seconds.The resistor element is made of aluminium and it has a uniform cross-sectional area with a diameter of 0,00016 inches.

hint: 1 inch=25,4 MN, resistivity of aluminium=2,825×10^-6 cm ohms

hint: 1 inch=25,4 MN, resistivity of aluminium=2,825×10^-6 cm ohms

Answer

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Answer:82.7 cm or 32.5 in

Explanation:The

required resistanceis calculated from therelationship of power,voltage, and resistance. Thewire lengthto give that resistance is calculated from ...L = A·R/ρ

The power is the ratio of energy to time:

P = E/t = (8 J)/(0.25 s) = 32 W

The required resistance is ...

R = V²/P = (240 V)²/(32 W) = 1800 Ω

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Then the required wire length is ...

L = (π/4)(0.00016 in × 2.54 cm/in)²×(1800 Ω)/(2.825×10^-6 Ω·cm)

L ≈ 82.65 cm

The length of aluminum wire required is about 82.7 cm or 32.5 in._____

Additional commentThis wire is roughly 66 AWG, about 1/6 the diameter of a human hair. Its melting current in still air is likely well below the current it carries in this heater. That is, it probably needs to experience significant airflow in order to maintain its integrity.