Question

A cylindrical conductor of length l and uniform area of cross section A has a resistance R. Another conductor of length 2l and resistance R of the same material must have the area of cross section.....................

Answer 1

Answer:

2A

Explanation:

The resistance of a wire can be defined as

R = ρL/A

Where,

ρ is Resistivity  - the factor in the resistance which takes into account the nature of the material is the resistivity

L is Length of the conductor

A is Area of cross section of the conductor.

R₁/R₂ = (L₁/L₂) × (A₂/A₁)  ----> rearranging it for A

A₂ = (R₁/R₂) × (L₂/L₁) × A₁  

A₂ = (R/R) × (2L/L) × A  

A₂ = 2A

Therefore, cross section area of another conductor must be 2A

Answer 2

Answer:

2A

Explanation:

The resistivity ρ = RA/l. Let R₁ = R, A₁ = A and l₁ = l be the initial resistance, cross-sectional area and length of material. If our length now becomes l₂ = 2l, R₂ = new resistance = R, A₂ = new area = ?. Since resistivity is constant,

R₁A₁/l₁ = R₂A₂/l₂

A₂ = R₁A₁l₂/R₂l₁ = RA(2l)/Rl = 2A

A₂ = 2A

Our new area is twice the old area.