Question

A piece of wire of resistance 20is drawn out so that its length is increased
to twice and area is reduced to half of its original value. Calculate the new
resistance and resistivity of this wire?


pls ab se may aur aap lok...koyi faltu answer nehi dega....i am not in the mood. so pls answer this questions​

Answer 1

GIVEN:

• Resistance of a wire = 20 ohm
• Length of the wire increased twice
• Area of cross-section reduced to half of its original value.

TO FIND:

• What is the new resistance and resistivity of the wire ?

SOLUTION:

We have given that, the resistance of a wire is 20 ohm

We know that the formula for finding the resistance of a wire, if length and area of cross-section have given is:-

$\large{\boxed{\bf{\star \: RESISTANCE = \rho \dfrac{L}{A} \: \star}}}$

According to question:-

$\bf{\longmapsto 20 = \rho \dfrac{L}{A} ....1) }$

Now, the length of wire increased twice and area of cross-section reduced by half of its original value

$\rm{\longmapsto R = \rho \dfrac{2 L }{\frac{A}{2}}}$

$\rm{\longmapsto R = \rho \dfrac{ 2 \times 2 L}{A}}$

$\rm{\longmapsto R = \rho \dfrac{4L}{A}}$

$\rm{\longmapsto R = \rho \dfrac{L}{A} \times 4 }$

$\rm{\longmapsto R = 20 \times 4 }$ [ From equation 1)]

$\bf{\longmapsto R = 80 \Omega }$

• New Resistance = 80 ohm

★ NEW RESISTIVITY ★

➺ Resistivity can only change by changing the temperature and Nature of material. Length and area of cross-section of the wire do not affect the Resistivity. So, the resistivity of the wire remains same.

______________________