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

Answer:

for copper potential difference is 2.4871 × $10^{-4}$ V

for silver  potential difference is 2.1256 × $10^{-4}$ V

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