Question

Resistance of a copper wire is 16 ohm find the resistance of another copper wire having double the length and half the area of cross section of the first one​

Answer 1

Answer:

Resistance is defined as the property of a material to show hindrance against the current flowing in the conductor. It always moves opposite in the direction of the current.

The expression for the resistance of a wire is given as,

R=ρlA where,

ρ is the resistivity of a material.

l is the length of wire.

A is the cross-sectional area.

In these types of questions, we will first find the resistance of wire having new length and divide it with the resistance of wire having original length so that we can find out the value of new resistance.

The resistance of wire having length (l) and area of cross-section (A) is given by-

R=ρlA

Now, on stretching a wire,

(a) volume of wire remains constant

(b) length of wire increases

(c) Area of cross section decreases

(d) Resistivity of wire remains constant.

If the length of the wire gets doubled, the new length of wire will be,

l′=2l

As the length of wire gets doubled, the cross-sectional area will become half of its previous value because volume of wire remains constant.

So, the new cross-sectional area becomes:

A′=A2

Now, the new resistance of the wire is given as:

R′=ρl′A′

Put all the values in formula, we get

⇒R′=ρ2lA2

⇒R′=4ρlA

Now we will divide new resistance with previous resistance,

⇒R′R=4ρlAρlA

⇒R′R=4

R′=4R

Hence, we can see that the new resistance is four times the previous resistance.