Question

A wire of resistance R was cut into two equal parts.Now one part is strechted to double the length.find the resistance of stretched wire

Answer 1

Given that,

Resistance = R

Length of half stretched wire = 2l

We know that,

The resistance is directly proportional to the length of the wire and inversely proportional to the area of wire.

If the length of the wire increases then the resistance will be increase.

In mathematically,

The resistance of the wire is

$R=\dfrac{\rho l}{A}$....(I)

Where, l = length

A = area

We need to calculate the resistance of stretched wire

Using formula of resistance

$R'=\dfrac{\rho l}{A}$

Put the value into the formula

$R'=\dfrac{\rho 2l}{A}$

Now, divided equation (I) by (II)

$\dfrac{R}{R'}=\dfrac{\rho l}{A}\times\dfrac{A}{\rho 2l}$

$\dfrac{R}{R'}=\dfrac{1}{2}$

$R'=2R$

So, if the length of the wire is double then the resistance will be double.

Hence, The resistance of stretched wire is double.

Answer 2

Given that,

Resistance = R

Length of half stretched wire = 2l

We know that,

The resistance is directly proportional to the length of the wire and inversely proportional to the area of wire.

If the length of the wire increases then the resistance will be increase.

In mathematically,

The resistance of the wire is

$R=\dfrac{\rho l}{A}$....(I)

Where, l = length

A = area

We need to calculate the resistance of stretched wire

Using formula of resistance

$R'=\dfrac{\rho l}{A}$

Put the value into the formula

$R'=\dfrac{\rho 2l}{A}$

Now, divided equation (I) by (II)

$\dfrac{R}{R'}=\dfrac{\rho l}{A}\times\dfrac{A}{\rho 2l}$

$\dfrac{R}{R'}=\dfrac{1}{2}$

$R'=2R$

So, if the length of the wire is double then the resistance will be double.

Hence, The resistance of stretched wire is double.

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