Question

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A wire of given material having length l and area of cross section A has a resistance of 4ohm. What would be the resistance of another wire of the same material having length l/2 and area of cross section 2A???
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Answer 1

Answer:

1 ohm

Step-by-step explanation:

The resistance of a wire is given by the formula:

R = (ρ * l) / A

where R is resistance, ρ is the resistivity of the material, l is the length of the wire, and A is the cross-sectional area of the wire.

Given that the wire has a resistance of 4 ohms, we can write:

4 = (ρ * l) / A

Multiplying both sides by A, we get:

4A = ρ * l

Now, consider the second wire with length l/2 and cross-sectional area 2A. Using the same formula, the resistance of this wire would be:

R' = (ρ * (l/2)) / (2A)

Simplifying, we get:

R' = (ρ * l) / (4A)

Substituting the value of ρ * l from the first equation, we get:

R' = (4A) / (4A)

R' = 1 ohm

Therefore, the resistance of the second wire would be 1 ohm