Problem 2: A silver wire 2m long is to have a resistance of 0.5 Ohm. What should its diameter be?
Ohm's law states that current flowing through any conductor is directly proportional to the potential difference V applied across the ends of the wire:
It is better to use R instead of conductance, known as resistance which is reciprocal of K.
using R above Equation will be:
Resistance of a conductor is directly proportional to its length and inversely proportional to its cross-sectional area. That is:
Solution:
Step: 1 Overview
Ohm's law:Ohm's law states that current flowing through any conductor is directly proportional to the potential difference V applied across the ends of the wire:
I is directly proportional to VResistance:
I = KV
where K is a constant known a conductance of the material of the wire.
It is better to use R instead of conductance, known as resistance which is reciprocal of K.
using R above Equation will be:
I=V/RResistance and its dependance upon resistivity:
Resistance of a conductor is directly proportional to its length and inversely proportional to its cross-sectional area. That is:
R = PL/AWhere P is a constant of proportionality known as resistivity of material. Resistivity has different values for different substances.
Step: 2 Calculation
Given:L=2mRequired:
R=0.5 Ohm
A= (Pi)r2
P of Silver = 1.52 x 10-8
d=?Solution:
We know that:
R = PL/A
A = PL/R
A=(1.52 x 10-8)(2)/(0.5)
A=6.08 x 10-8
(Pi)r2=6.08 x 10-8
(3.14)r2=6.08 x 10-8
r2=(6.08 x 10-8)/3.14
r2=1.93 x 10-8
r=1.39 x 10-4m
d=2r=2(1.39 x 10-4m)
d=2.78 x 10-4m (Ans)
