A wire of 4 ohm is doubled to its length and half of diameter what will be the new resistance?

Question

Answer

R=p l/A
=4 ohm

Now,

p=p'
l/2=l'
2A=A'

so,
R'=p' l'/A'
=p(l/2)/2A
=1 ohm

Answer

Answer

Explanation:

To determine the new resistance of the wire, we need to consider the effect of doubling the length and halving the diameter on the wire's resistance.

1. Resistance and Length:
Resistance is directly proportional to the length of the wire. When the length of the wire is doubled, the resistance also doubles. This can be explained by the formula for resistance:

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.

In this case, since the length is doubled, the resistance will also double.

2. Resistance and Cross-Sectional Area:
Resistance is inversely proportional to the cross-sectional area of the wire. When the diameter of the wire is halved, the cross-sectional area is reduced by a factor of four (since area is proportional to the square of the diameter). This can be explained by the formula for the area of a circle:

A = π * (d/2)^2

Where A is the cross-sectional area, π is a constant (approximately 3.14), and d is the diameter of the wire.

Thus, when the diameter is halved, the cross-sectional area becomes one-fourth of the original value.

3. Calculation:
Since the length is doubled and the diameter is halved, the resistance will be affected by both factors.

Doubling the length will double the resistance, while halving the diameter will reduce the resistance to one-fourth of the original value.

Therefore, the net effect on the resistance can be calculated by multiplying the two factors:

Net resistance = (2 * original resistance) * (1/4 * original resistance)
= original resistance / 2

Hence, the new resistance will be half of the original resistance.

In this case, the original resistance is 4 ohms, so the new resistance will be:

New resistance = 4 ohms / 2
= 2 ohms

Thus, the new resistance of the wire after doubling its length and halving its diameter will be 2 ohms.

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