Help me solve a question about conductor's wire

[keni4eva]

A conductor of 0.5mm diameter wire has a resistance of 300Ω. Find the resistance of the same length of wire if its diameter were doubled.

 

[the_risk_master]

Re: PLS HELP

R = (ρL)/A

where: ρ - resistivity constant of the material
L - length of the material
A - cross-sectional area of the material at length

since: L1 = L2 and ρ1 = ρ2

and A = (pi×D²)/4 ---- circular area

thus:

(R1×A1) = (R2×A2)


R2 = R1 (A1/A2)

R2 = R1 ( (D1)²/(D2)²)

but:

D2 = 2×(D1)

R2 = R1 ( (D1)²/(2×D1)²) ---- D1 cancels

R2 = R1 / (2²) = R1 /4

R2 = (300Ω)/4

R2 = 75Ω


Very elementary!

 

[forkschgrad]

Re: PLS HELP

way to go