Question

4. The length of a wire is doubled. By what factor does
the resistance change
(a) 4 time as large
(b) twice as large
(c) unchanged
(d) half as large
​

Answer 1

Answer:

b twice as large

Explanation:

resistance is directly proportional to the length of the conductor and inversely proportional to the crossectional area of the conductor. so doubling the length doubles the resistance.

Answer 2

Question : -

The length of a wire is doubled. By what factor does the resistance of the wire changes ?

• a) 4 times as large
• b) twice as large
• c) unchanged
• d) half as large

Answer

Given : -

Length of a wire is doubled

Required to find : -

• Change in resistance ?

Formula used : -

R = ρ*L/A

Here,

• R = Resistance
• ρ = Specific resistance
• L = length of a conductor
• A = Area of cross-section

Solution : -

It is given that,

Length of a wire is doubled

We need to find the change in resistance ..

So,

Here he didn't mentioned any information about specific resistance or area of cross-section ..

We will assume those parameters to be constant.

Case - 1 (when all factors are constant)

Let,

Length of wire be l

Area of cross-section = A

specific resistance = ρ

Resistance (R1) = ρ*l/A »(1)

Case - 2(when length is doubled)

Length of wire after doubling it's length = 2l

Area of cross-section = A

specific resistance = ρ

Resistance (R2) = ρ*2l/A »(2)

Divide 1 by 2

R1 : R2 = ρ*l/A : ρ*2l/A

R1 : R2 = 1 : 2

From here,

The wire whose length is doubled its resistance is also doubled (twice as large)

Option - B is correct ✓