Question

If the length of a conductor and its radius is increased twice, how the resistance will change?
1. Resistance will remain unchanged
2. Resistance increase twice
3. Resistance will become half
4. Resistance will increase 4 times

Answer 1

Answer:

Resistance will increase twice

Answer 2

Answer:

If the length of a conductor and its radius is increased twice then the resistance will become half i.e.option(3).

Explanation:

We will use the following formula to solve this question,

$\mathrm{R\propto \frac{L}{r^2} }$                   (1)

Where,

R=resistance of the conductor

L=length of the wire

r=radius of the wire

We can also write equation (1) we get:

$\mathrm{\frac{R}{R_2} =\frac{L_1r_2^2}{L_2r_1^2} }$                 (2)

R=initial resistance of the conductor

R₂=final resistance of the conductor

L₁=initial length of the wire

L₂=final length of the wire

r₁=initial radius of the wire

r₂=final radius of the wire

In the question, it is given that both the length and radius are increased twice. So, equation (2) can also be written as,

$\mathrm{\frac{R}{R_2} =\frac{L\times (2r)^2}{2L\times (r)^2} }$

$\mathrm{\frac{R}{R_2} =\frac{L\times 4r^2}{2L\times r^2} }$

$\mathrm{\frac{R}{R_2} =2}$

$\mathrm{R_2=\frac{R}{2} }$                (3)

Hence, from equation (3) we can deduce that the resistance will become half i.e.option(3).

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