When a cylindrical wire made of a new alloy is stretched to double its original length, its resistance increases by a factor of four. If a second wire of the same alloy is shaped into a flat ribbon of identical length but half the original cross-sectional area, which property stays constant between the two wires?
The specific resistance remains unchanged for both wires
Resistance of a conductor is \(R = \frac{\rho L}{A}\), where ρ is the specific resistance (resistivity) of the material.
Stretching or reshaping a wire changes L and A, so R changes; the fourfold rise on doubling the length is only due to L doubling and A halving.
Resistivity ρ depends only on the material and its temperature, not on its shape or dimensions. Both wires are made of the same alloy, so ρ is the same for both.
The other properties change: resistance depends on L/A, so it differs between the two shapes; current-carrying capacity depends on cross-sectional area and cooling surface; and the voltage drop for a given current is IR, which changes with R.
Hence, the answer is The specific resistance remains unchanged for both wires.
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Important Questions from Resistance and Resistivity
Which of the following metals has the lowest electrical resistivity?
A uniform wire of resistance 9Ω is bent in the form of an equilateral triangle. Find the effective resistance across a side of the triangle.
The value of carbon resistance is 54 × 103 Ω. The percentage tolerance is 5%. What is the colour code sequence of carbon resistance?
Which of the following relations are wrong?
I. The specific conductance is given by the relation \(k = \frac{1}{R}\left( {l/A} \right)\)
II. The equivalent conducting is given by the relation \(\lambda = \frac{{100\;K}}{C}\)
III. The specific resistance is given by the relation \(\rho = \frac{{Rl}}{A}\)
A current is flowing through a metallic wire. If the wire is heated, which quantities change?
