Question

The resistance of a wire is 24 ohm. What will be the new resistance if

(a) only the length of the conductor is increased to 3 times of its original length.

(b) only the cross section area of the wire is doubled?

Answer 1

Step 1: Given that:

The resistance(R) of the wire= 24Ω

Step 2: a) Calculation of new resistance when only the length is increased to 3 times:

Let the original length of the wire is $l$ , then

We know that;

Resistance of a conductor $\propto$ the length of the conductor.

Thus,

If only the length of the conductor is increased by 3 times, its resistance will also be increased by 3 times.

Therefore the new resistance = $3R$

= $3\times 24\text{Ω}$

= $72\text{Ω}$

Step 3: Calculation of new resistance when only the area of cross-section is doubled:

The resistance of a conductor is inversely proportional to the area of cross-section of the conductor.

That is;

$R\propto \frac{1}{A}$

Thus,

As the area of the cross-section is doubled, the resistance of the conductor will be halved.

Thus,

New resistance= $\frac{24\text{Ω}}{2}=12\text{Ω}$

Thus,

The new resistance when only length is incresed= $72\text{Ω}$

when only area of cross-section is increased= $12\text{Ω}$