Question

A 14.0 gauge copper wire of diameter 1.628 mmcarries a current of 14.0 mA. Part A: What is the potential difference across a 2.15 mlength of the wire?

Part B: What would the potential difference in part A be if the wire were silver instead of copper, but all else was the same?

Answer 1

for copper potential difference is 2.4871 ×
`10^(-4)` V

for silver potential difference is 2.1256 ×
`10^(-4)` V

Step-by-step explanation:

given data

diameter D = 1.628 mm = 0.001628 m

current = 14.0 mA = 0.0140 A

length L = 2.15 m

to find out

potential difference

solution

we consider here

resistivity of silver = 1.47 ×
`10^(-8)` ohm-m

resistivity of copper = 1.72 ×
`10^(-8)` ohm-m

so we apply here resistance formula that is

Resistance = ρ × L / A ...............1

so here area A = πr² = π(0.001628 /2)² = 2.0816 ×
`10^(-6)` m²

for copper Resistance = ρ × L / A

Resistance = 1.72 ×
`10^(-8)` × 2.15 / 2.0816 ×
`10^(-6)`

Resistance = 1.7765 ×
`10^(-2)` ohm

for silver Resistance = ρ × L / A

Resistance = 1.47 ×
`10^(-8)` × 2.15 / 2.0816 ×
`10^(-6)`

Resistance = 1.5183 ×
`10^(-2)` ohm

so

potential difference is calculated as

for copper potential difference = current × resistance

potential difference = 0.0140 ×1.7765 ×
`10^(-2)`

potential difference = 2.4871 ×
`10^(-4)` V

for silver potential difference = current × resistance

potential difference = 0.0140 × 1.5183 ×
`10^(-2)`

potential difference = 2.1256 ×
`10^(-4)` V