Question

The resistance of wire is 12 ohm. What is the resistance of another wire of same material -
but length twice of the first wire and radius also equal to 2 times the radius of the 1"
wire?
​

Answer 1

this is the answer

Explanation:

R=12ohm

we know R is directly proportional to length/area

new R= pL/A

=2pL/π4=1/2R

=1/2×12

=6ohm

Answer 2

Answer:

Resistance of wire with length twice of first wire(with resistance 12Ω) and radius twice the radius of first wire is 6Ω

.Explanation:

Resistance of wire is directly proportional to length of wire and inversely proportional to cross sectional area .

so we have

R ∝ $\frac{L}{A}$

R = ρl/A

Given : R of wire = 12 Ω    

       R of another wire of same material with L₂= 2L and r₂= 2r.

Step 1:

resistance of first wire

 R = ρ L/ πr²

12 = ρL/ πr²  

so , ρ  = 12πr²/L  --------------(i)

Step 2:

resistance of second wire

R ₂ = ρL₂/πr₂²

substituting ρ from above equation

R₂= 12πr²L₂/πr₂²L₁

on substituting values from given data

R₂ = 12r²2L₁/4r²L₁

R₂= 6 Ω

Hence resistance is 6Ω.