A uniform wire of resistance 4 ohm is cut into two equal lengths. Each...
**Solution:**
To solve this problem, we need to understand the concept of resistance and how it changes when the length and cross-sectional area of a wire are altered.
**Resistance of a wire:**
The resistance of a wire is given by the formula:
R = (ρ * L) / A
where R is the 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.
**Resistivity:**
The resistivity of a material is a constant that depends on the material's properties. It is denoted by the symbol ρ.
**Length and resistance:**
If the length of a wire is doubled while keeping the cross-sectional area constant, the resistance of the wire also doubles. This can be derived from the resistance formula:
R' = (ρ * 2L) / A = 2 * (ρ * L) / A = 2R
where R' is the new resistance.
**Dividing the wire into two equal lengths:**
When the uniform wire is cut into two equal lengths, each length will have half the original length of the wire.
**Drawing the wire to twice its length:**
When each wire is drawn to twice its length, the new length will be double the original length.
**Calculating the resistance of each wire:**
Since the resistance of a wire doubles when its length is doubled, and each wire is drawn to twice its length, the resistance of each wire will be four times the original resistance. This can be derived as follows:
R' = 2R (doubling the length)
R'' = 2R' = 2(2R) = 4R
Therefore, the resistance of each wire will be four times the original resistance, which is 4 ohms.
**Conclusion:**
The correct answer is option (c) 4 ohm.