Question

a wire of length L the resistance R is stretched so that its length is doubled and the area of cross section is halved how will its resistance change and
resistivity change​

Answer 1

$\huge{ANSWER}$

▶Length =L

▶Area of cross section =A

▶Resistance = R

So,

✳Resistance =$\rho \frac{Length}{Area of cross section }$

✳R=$\rho \frac{L}{A}$

According to the question, the wire is being stretched to double so,

▶New Length =2L

◼Resistance is directly proportional to length so if length increase resistance might also have increased.

$R\propto L$

▶New area of cross section =$\frac{A }{2}$

◼Resistance is inversely proportional to area of cross section so if area of cross section decreases resistance might have increased.

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

Let the new resistance be R1.

✳Resistance =$\rho \frac{Length}{Area of cross section }$

✳R1=$\rho \frac{2L}{\frac{A}{2}}$

On dividing the original resistance by New resistance,

▶$\frac{R}{R1}=\rho \frac{L}{A} \div \rho \frac{2L}{\frac{A}{2}}$

▶$\frac{R}{R1}=\frac{L}{A}\times \frac{\frac{A}{2}}{2L}$

▶$\frac{R}{R1}=\frac{L}{A}\times \frac{A}{4L}$

ON SOLVING,

▶$\frac{R}{R1}=\frac{1}{4}$

▶R1=4R.

So, the new resistance will be four times the original resistance.

◼RESISTIVITY

The resistivity won't be altered as it doesn't depends on length of area of cross section.It only depends on nature and the temperature of the material.