Question

Resistance of a given wire of length 'l' is 4.the wire is stretched uniformly such that its length becomes 3l. Find the new resistance of the stretched wire

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Answer 1

Concept:

An obstacle to current flow is what is referred to as resistance. To convert electrical energy into light, heat, or movement, a circuit must have resistance. Mathematically, resistance can be expressed as, Resistance, R = ρl/A

Given:

Length of given wire = l

Resistance of wire with length 'l' = 4 ohm

The new length of wire = 3l

Find:

We need to determine the new resistance of the stretched wire when its length becomes 3l.

Solution:

We know,

Resistance, R = ρl/A where R is the resistance, ρ is the resistivity, l is the length of the wire and A is the area of the cross-section of the wire.

We have, R = 4ohm

Therefore, R = ρl/A = 4

Now, we have a new length = 3l

Substitute in the equation of resistance, l = 3l

R = ρ3l/A

R = 3 × ρl/A

We know, ρl/A = 4

R = 3 × 4

R = 12 ohm

Thus, the new resistance of the stretched wire is 12 ohms.

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Answer 2

Answer:

New resistance is $12$ ohms.

Explanation:

Resistance is defined as hinderance to the flow of current.

It is given that Length of given wire = l

Length 'l' is stretched and becomes = 4 ohm

The new length of wire = 3l

We need to determine new resistance.

Mathematically

Resistance is directly proportional to length.

If Resistance of wire with length 'l' = 4 ohm

Then after stretching, resistance will also, increase by same amount.

Hence, if resistance is 4 ohm, after wire is stretched uniformly such that its length becomes 3l,

new resistance becomes $4*3=12$

New resistance is $12$ ohms.

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