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
- 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:
- Resistivity of the wire depends on mainly ________
When a number of resistance are connected in _______, their combined resistance is less than the smallest individual resistance.
Important Questions from Resistance and Resistivity
Which of the following statements are correct about the electrical resistance and resistivity of a wire?
1. Both quantities depend on the area of cross-section of the wire
2. Both depend on the temperature
3. Resistance of the wire is directly proportional to the resistivity of the wire
4. Resistivity of the wire is directly proportional to the length of the
wireSelect the correct answer using the code given below:
A circular coil of single turn has a resistance of 20 Ω. Which one of the following is the correct value for resistance between the ends of any diameter of the coil?
Let us consider a copper wire having radius r and length l. Let its resistance be R. If the radius of another copper wire is 2r and the length is l/2 then the resistance of this wire will be
If the length of a conductor is doubled, then the resistance of the conductor will be: (other parameters are kept same)
Which factor does NOT affect the resistivity of a material?
