# A uniform wire of resistance 100ohms is melted & recast into a wire of half length & double cross sectional area that of the original.What would be the resistance of new wire formed?

2
Log in to add a comment

Log in to add a comment

When the length of the wire is halved, the resistance is also halved and when its area is doubled also, its resistance is further halved and becomes 1/4 th of the original value.

Thus, the resistance of the new wire is 1/4 of 100 ohms = 25 ohms.

The volume of the wire remains same when it is recast.

A₂ = 2 *A₁ and L₂ = L₁ / 2

Resistance R = ρ * L / A

R₂ = ρ L₂ / A₂ = ρ L₁ / (2 2 A₁) = R₁ / 4 = 100 Ω / 4 = 25 Ω

Hence resistance becomes 1/4 th.

You can also say that, resistance is proportional to the length and inversely proportional to the area of cross section. Hence, the resistance becomes 1/2 * 1/2 times initial.

A₂ = 2 *A₁ and L₂ = L₁ / 2

Resistance R = ρ * L / A

R₂ = ρ L₂ / A₂ = ρ L₁ / (2 2 A₁) = R₁ / 4 = 100 Ω / 4 = 25 Ω

Hence resistance becomes 1/4 th.

You can also say that, resistance is proportional to the length and inversely proportional to the area of cross section. Hence, the resistance becomes 1/2 * 1/2 times initial.