The length, cross-sectional area and material of the wire
The correct answer is 2. The length, cross-sectional area, and material of the wire.
The resistance (R) of a wire is determined by its physical properties according to the formula:
\( R = \rho \frac{L}{A} \)
Where:
- \( R \) is the resistance (in ohms, Ω)
- \( \rho \) is the resistivity of the material (in ohm-meters, Ωm) - this accounts for the material's inherent ability to conduct electricity.
- \( L \) is the length of the wire (in meters, m)
- \( A \) is the cross-sectional area of the wire (in square meters, m²)
This formula clearly shows that resistance is directly proportional to the length of the wire (\(L\)) and inversely proportional to its cross-sectional area (\(A\)). A longer wire has more resistance, while a thicker wire (larger area) has less resistance. The resistivity (\(\rho\)) is a material property and different materials have different resistivities. For example, copper has a much lower resistivity than nichrome, meaning copper wires have lower resistance for the same dimensions.
Therefore, all three factors – length, cross-sectional area, and material – influence the resistance of a wire.
Similar Questions
If the length of a resistor is doubled, what happens to its resistance, assuming all other factors remain constant?
- The resistance of a particular material wire with length L and cross-sectional area A is 2 Ω. What would be the resistance of another wire of the same material having length 2L and area of cross-section A/2?
- The resistance of a uniform metallic conductor depends on its:
- Which of the following statements is correct?
A cylindrical wire of length L and radius r has resistance R. The resistance of another wire of the same material but of twice its length and one-fourth its radius is:
- A cylindrical wire of length L and radius r has a resistance R. The resistance of another wire of the same material but half its length and half its radius will be:
- The length and the cross-sectional area of a conductor in the shape of a cylinder are '\(l\)' and '\(A\)' respectively. The resistivity of the material of the conductor is '\(\rho\)'. Its resistance depends upon
(p) \(l\) only
(q) \(l\) and \(A\)
(r) \(\rho\), \(l\) and \(A\)
(s) \(\rho\) and \(l\), but not \(A\)
Pick up the right option from those given above. - Resistivity of the wire depends on mainly ________
- The resistance of a metallic wire of length 1m and area of cross-section 1sq.metre having a resistivity is $2 \times 10^{-6}$ ohm - m is:
- A cylindrical wire of length \(L\) and radius \(r\) has a resistance \(R\). The resistance of another wire of same material but having four times its length and half its radius will be:
Important Questions from Resistance and Resistivity
Which of the following metals has the lowest electrical resistivity?
When electric current is passed through a wire, the amount of heat produced in a wire depends upon _______.
I. Length
II. Thickness
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 \(\rho = \frac{{Rl}}{A}\)
