Answer to Question #73947 in Electricity and Magnetism for Ayrill

Question

2. A wire 100cm long and 2mm in diameter has a resistivity of 4.8x10
-8Ωm.
(i) Calculate the resistance of the wire?
(ii) A second wire of the same material has the same weight as the 100m length, but twice its diametric. Evaluate its resistance.

Answer 1

The electrical resistance R is defined as:

R=ρ l/A
where
R is the electrical resistance of a uniform specimen of the material (measured in ohms, Ω)
ρ is the electrical resistivity (Ωm)
l is the length of the piece of material (measured in metres, m)
A is the cross-sectional area of the specimen (measured in square metres, m2).

(i)
A_1=(πd^2)/4=π×(2×〖10〗^(-3) m)^2/4=3.14×〖10〗^(-6) m^2

R_1=(4.8×〖10〗^(-8) Ωm) (1 m)/(3.14×〖10〗^(-6) m^2 )=0.015 Ω

(ii)
l_2=100 m;
A_2=(πd_2^2)/4=π×(4×〖10〗^(-3) m)^2/4=12.57×〖10〗^(-6) m^2
R_2=(4.8×〖10〗^(-8) Ωm) 100/(12.57×〖10〗^(-6) m^2 )=0.38 Ω


Answer: (i) 0.015 Ω; (ii) 0.38 Ω.