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[1]
Is it true that if a given amount of current is passed through two wires of length $10 cm$ and $5 cm$ of the same material and cross-section, then the amount of heat produced by both wires is the same?

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True

False

answer is B.

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Detailed Solution

The above statement is False.
We have

H = I^{2} R

, where

H

is the heat produced,

I

is the current flowing through the wire, and

R

is the resistance of the wire. The amount of heat produced by a wire depends upon the resistance of the wire. Therefore,

H \propto R

, when current is constant.
We have

R \propto \frac{l}{a}

, where

R

is the resistance of the wire,

l

is the length of the wire, and

a

is the area of the cross-section of the wire. So, the resistance of the wire is directly proportional to the length of the wire. Thus, the resistance of a wire of length

10 cm

will be more than that of a wire of length

5 cm

.
The correct statement would be that if a wire of length

10 cm

and a wire of length

5 cm

of the same material and cross-section, when arranged in two different circuits, the amount of heat produced by both the wires is not the same.

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