Question

what happens to resistance if its length is half and its area become double​

Answer 1

Answer:

Becomes 1/4 times of original resistance.

☸Given☸

• Length of the wire is halved
• Area of the wire is doubled

Considering given conductor as wire

☛ To Find:

• Effect on resistance of wire

✺Solution✺

$\rule{200}{2}$

We know that,

Resistance of wire, $\bf{R=\dfrac{\rho\:l}{A}}$

where,

• R = Resistance of wire  
• ρ = Resistivity of wire
• l = length of wire
• A = Area of wire

$\rule{200}{2}$

Let original resistance of wire  be R

So,

$\longrightarrow\sf{R=\dfrac{\rho\:l}{A}}$

After halving the length and doubling the area of wire, we get

$\longrightarrow\sf{R'=\dfrac{\rho\:\bigg(\dfrac{l}{2}\bigg)}{2A}}$

$\longrightarrow\sf{R'=\dfrac{\rho\:l}{2\times2A}}$

$\longrightarrow\sf{R'=\dfrac{\rho\:l}{4A}}$

$\longrightarrow\sf{R'=\dfrac{1}{4}\bigg(\dfrac{\rho\:l}{A}\bigg)}$

$\longrightarrow\sf{\pink{R'=\dfrac{1}{4}R}}$

Hence, new resistance becomes  $\green{\dfrac{1}{4}}$ times of original resistance.