Question

Electrical resistance ina wire is directly proportional to its length and inversely proportional to the square of its diameter. If a 10 cm long wire with diameter 2 cm had a resistance 600 ohms, a 15 fm long wire with diameter 5 cm has resistance

Answer 1

Initial Conditions:

length=L= 10 cm = (10*10⁻²)m
Diameter=D= 2 cm= (2*10⁻²)m
Radius= r= 0.01m
Area=A= π*r²/2 =1.57*10⁻⁴ m²

Resistance=R= 600 ohm

So, from initial conditions we find resistivity(р)
R=рL/A
R*A /L=р
(600)*(1.57*10⁻⁴)/(10*10⁻²)=р
р=0.942 Ω m
As, material remains same so resistivity(p) doesn't change

Lenght= L1= 15 fm= 15*10⁻¹⁵ m
Diameter= D1 = 5 cm= 5*10⁻² m
Radius= r= 0.025 m
Area= A1= π*r²/2 =9.8125*10⁻⁴ m²
R=р*L1/A1
R=(0.942 )*(15*10⁻¹⁵ )/(9.8125*10⁻⁴)
R=1.44*10⁻¹¹ Ω