A given conductor carrying a current of 1 A produces an amount of heat

A given conductor carrying a current of 1 A produces an amount of heat equal to 2000 J. If the current through the conductor is doubled, the amount of heat produced will be

2000 J

4000 J

8000 J

1000 J

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Answer is Wrong!

This question was previously asked in

UPSC NDA-1 – 2016

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The amount of heat produced will be 8000 J.

According to Joule’s Law of Heating, the heat produced (H) in a resistor is directly proportional to the square of the current (I), the resistance (R), and the time (t) for which the current flows: H = I²Rt. Assuming the resistance of the conductor and the time duration are constant, the heat produced is proportional to the square of the current (H ∝ I²).
Given that H1 = 2000 J for I1 = 1 A.
When the current is doubled, I2 = 2 * I1 = 2 A.
The new heat produced H2 will be proportional to (I2)²:
H2 / H1 = (I2)² / (I1)²
H2 / 2000 = (2I1)² / (I1)²
H2 / 2000 = 4 * (I1)² / (I1)²
H2 / 2000 = 4
H2 = 4 * 2000 J = 8000 J.

Joule’s law explains why wires and electrical components heat up when current passes through them. This principle is used in various applications like electric heaters, toasters, and fuses. The power dissipated as heat is given by P = I²R, and the total heat produced over time t is H = Pt = I²Rt.

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