Question

The greater the diameter of the wire used in the household wiring, the greater the maximum current that can safely be carried by the wire. Why is this? Does the maximum permissible current depend on the length of the wire? Does it depend on what the wire is made of? Explain your reasoning.

Answer 1

The current carrying capacity of cables depends on:
Conductor material (copper, copper aloy, aluminium, steel)
Surface treatment of the conductor (plain, tinned, silver plated, nickel plated)
Condcutor cross section
Thermal capacity of the insulation material
Ambient temperature
Installation mode (free in the air, in cable trays, in earth)
Accumulation (single core, several cores spaced, bundles)
Other ambient effects (sun-radiation, UV)

vd =	Drift Velocity (SI: m/s)
rn =	Number Density - Charges per unit Volume (SI: #/m 3) (The text uses n for this symbol, don't confused it with # moles)
q =	Magnitude of the charge on each moving charge (SI: C) (Typically q = e = 1.602x10 -19 C, charge on an electron)
A =	Cross-sectional Area perpendicular to the flow. (SI: m 2)

It is directly proportional to cross sectinal area which inturn is proportional to diameter.

It is independent of length wire. Ofcourse it is depend on type of wire as drift velocity is different for different material.

Answer 2

• Current does not actually flow through a wire, but rather along it surface. As such, the larger a wire's gauge, the greater its surface area and the greater its electrical capacity. Stranded wire, by virtue of its having more combined surface area, has a greater capacity than solid wire of the same diameter.

Length

• As electricity travels along a wire's surface, it faces resistance and loses energy. The longer the distance, the larger the wire's gauge must be to increase the capacity enough to have a sufficient amount of current reach the end of the wire.

• yes it depends on the material of the wire the resistance faced by the wire depends on the resistivity of the material used more the resistance of the wire, and resistance of the wire is inversely proporatinal to the amount of electricity that caan pass, and resistance is also directly proportatinal to the heat produced in the wire for the given current.

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