Question 417.
Two cylindrical wires of identical length are made of copper and iron. If they carry the same current and have the same potential difference across their length, what is the ratio of their radii (copper/iron)?
Answer 417.
Same p.d. and same current => same resistance
Resistance of copper wire = ρl/πr^2
and resistance of iron wire = ρ'l/πr'^2
where ρ and ρ' are resiistivity of copper and iron respectively
and r and r' are the radii of the copper and iron wires respectively
As they have the same resistance,
ρl/πr^2 = ρ'l/πr'^2
=> (r/r')
= √(ρ/ρ')
= √(1.68x10^-8)/(10 x 10^-8)
= 0.41
Link to YA!
Two cylindrical wires of identical length are made of copper and iron. If they carry the same current and have the same potential difference across their length, what is the ratio of their radii (copper/iron)?
Answer 417.
Same p.d. and same current => same resistance
Resistance of copper wire = ρl/πr^2
and resistance of iron wire = ρ'l/πr'^2
where ρ and ρ' are resiistivity of copper and iron respectively
and r and r' are the radii of the copper and iron wires respectively
As they have the same resistance,
ρl/πr^2 = ρ'l/πr'^2
=> (r/r')
= √(ρ/ρ')
= √(1.68x10^-8)/(10 x 10^-8)
= 0.41
Link to YA!
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