Question

a lead wire and iron wire are having same dimension their respective specific resistance are in the ratio 49:24 the ratio of their resistance is​

Answer 1

Given:

ρ_lead : ρ_iron = 49 : 24

l_lead = l_iron = l

A_lead = A_iron = A

To find:

The ratio of their resistance

Solution:

Resistance (R)

R = ρ × (l / A)

R_lead = ρ_lead × (l_lead / A_lead)

R_lead = ρ_lead × (l / A)                              - equation (1)

R_iron = ρ_iron × (l_iron / A_iron)

R_iron = ρ_iron × (l / A)                              - equation (2)

Divide equation (1) and (2)

We get,

R_lead / R_iron = ρ_lead / ρ_iron

It is given that ρ_lead / ρ_iron = 49/24

Therefore, R_lead / R_iron = 49/24

So, R_lead : R_iron = 49 : 24

Therefore, the ratio of resistance of lead wire and the iron wire is 49:24