The resistance \(R\) of a wire is given by the formula:
\(R = \frac{\rho L}{A}\)
where:
- \(\rho\) is the resistivity of the material (constant for the same material)
- \(L\) is the length of the wire
- \(A\) is the cross-sectional area of the wire
For the first wire, we have \(R_1 = 2 \Omega\), \(L_1 = L\), and \(A_1 = A\).
For the second wire, we have \(L_2 = 2L\) and \(A_2 = A/2\). We want to find \(R_2\).
Using the formula for resistance:
\(R_1 = \frac{\rho L_1}{A_1} = \frac{\rho L}{A} = 2 \Omega\)
\(R_2 = \frac{\rho L_2}{A_2} = \frac{\rho (2L)}{A/2} = \frac{4\rho L}{A}\)
Since \(R_1 = \frac{\rho L}{A} = 2 \Omega\), we can substitute this into the expression for \(R_2\):
\(R_2 = 4 \times \frac{\rho L}{A} = 4 \times R_1 = 4 \times 2 \Omega = 8 \Omega\)
Therefore, the resistance of the second wire is 8 Ω.
Similar Questions
- Which of the following statements is correct?
- 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:
- 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 resistance of a 10 m long copper wire is R ohm. What will be the resistance of a 5 m long copper wire?
When a number of resistance are connected in _______, their combined resistance is less than the smallest individual resistance.
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:
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?
