Question

(a) List the factors affecting resistance of a conductor. (b) Calculate the length of Cu wire of diameter 3mm required to make a conductor of resistance 10Ω. Resistivity of Cu is 1.6x 10-8 Ωm.

Answer 1

Hi,

Here is your answer

a)Factors affecting resistance of a conductor

• Nature of conductor
• Temperature: In case of metallic conductors, when temperature increases, resistance increases and vice versa. In case of semi conductors when temperature increases, resistance decreases and vice versa.
• Length of the conductor: When length increases, resistance increases and vice versa
• Area of cross section: When area of cross section increases,resistance decreases and vice versa.

b)

Given:

Diameter of the wire=3mm=0.003m

Resistance(R)=10Ω

Resistivity(ρ)=1.6×10^-8Ωm

To Find:

Length of the conductor(l)

Solution:

We know that

Resistance=ρl/A

l=R(A/ρ)

Radius of the wire=diameter/2=0.003/2

Radius=0.0015m

Area of cross section=πr²

Area=3.14×0.00015×0.00015

Area=7.065×10^-8 m²

Substitute the given datas in the above equation

We get,

l=10(7.065×10^-8)/1.6×10^-8

Length of the conductor=44.15m

Notes:

1. Remember to convert all the datas given to their SI units before calculating.

2. Resistivity does not depend on area and length of the conductor.

Hope this helps you.