Question

A given length of a wire is doubled and this
cess is repeated once again. By what factor does
the resistance of the wire changes with steps​

Answer 1

Answer:

Resistance of a wire is directly proportional to the length of the wire. As its length increases it's resistance increases.

Let x be the resistance of a wire of length L

If length of a wires is doubled to 2L its resistance is doubled to 2x

If it is doubled again, the length of the wire becomes 4L and it's resistance becomes 4x.

Thus if a given length of a wire is doubled on itself and this process is repeated once again it's resistance increases by a factor of 4

Answer 2

$\red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}$

Resistance is the Opposition force offered by a conductor when current passes through it.

Heating effect of electric current takes place because of the resistance of conductor .

Resistance of a conductor is directly proportional to it's length and inversely proportional to it's cross sectional area.

$\blue{\mid{\underline{\overline{\textbf{Coming to question :-}}}\mid}}$

We have been asked that the length of wire is double and the same process is repeated once again, then at the end what whill be the change in resistance of conductor. We have to find change in resistance.

Now let's say that the Resistance of conductor is R. And the length of conductor as H.

In first case the length is doubled, now we know resistance of a conductor is directly proportional to length of conductor, thus if length of conductor is increased by x cm then the resistance will also increase by x ohm.

Now in the first case, length of conductor is doubled = H × 2.

Now since length is directly proportional to resistance then in first case resistance will also get doubled.

$\bigstar \: \orange{\mid{\underline{\overline{\textbf{2H = 2r}}}\mid}}$

Now , it is given that this process is repeated once again,

Now in this case 2H will be doubled and it will become 4H , since length is directly proportional to resistance thus, 2r will also be doubled and therefore resistance now will be 4 times more than it was at starting.

$\bigstar \: \orange{\mid{\underline{\overline{\textbf{4H = 4r}}}\mid}}$

Therefore at the end resistance of conductor will become 4 times more than it was at starting.

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BY SCIVIBHANSHU

THANK YOU

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