Question

A wire of length g and area of cross section A has a resistance of 10 ohms. What will be the resistance of the wire if the length is doubled?

Answer 1

resistance of wire is directly proportional to its length nd inversely proportional to its cross sectional area...

so by doubling the length .... resistance will also get doubled..

new resistance = 20 ohm

Answer 2

Correct Question

A wire of length 'l' and area of cross section 'A' has a resistance of 10 ohms. What will be the resistance of the wire if the length is doubled?

Solution-

Resistance of a wire is directly proportional to length of the wire and inversely proportional to the area of cross-section i.e. R ∝ l/A

If we remove the sign of proporinalty then there comes a constant i.e. p (rho = resistivity).

R = p l/A ................(1st equation)

As per given condition,

Length is doubled. If length is doubled then resistance also become doubled and area of cross-section becomes half.

Let's denote the new resistance by R'.

R' = p 2l/(A/2)

R' = p 4l/A

R' = 4 p l/A

Using 1st equation, we can say that

R' = 4R ...............(2nd equation)

And given in question that, resistance of wire is 10 ohm. Means R = 10 ohm.

So, substitute the value of R in (2nd equation)

R' = 4(10)

R' = 40 ohm

Therefore, the new resistance is 40 ohm.