Question

1-What four physical factors affect the resistance of a wire?

2-A wire of uniform cross-section has a resistance of R. What would be the resistance of a similar wire, made of the same material, but twice as long and of twice the diameter?

3- A block of carbon, 1.0 cm by 2.0 cm by 5.0 cm, has a resistance of 0.015 Ω between its two smaller faces. What is the resistivity of carbon?

4-What length of German silver wire, diameter 0.050 cm, is needed to make a 28 Ω resistor, if the resistivity of German silver is 2.2 x 10-7 Ω.m?

5-What is the resistance of one kilometer of copper wire (copper resistivity is 1.68x10-8 Ω.m), with a diameter of 10 cm.

Answer 1

1. There are 4 different factors which affect resistance:

• The type of material of which the (wire) resistor is made.
• The length of the resistor. Resistance inreases with the length of the resistor.
• The thickness of the resistor. Resistance decreases as the thickness of the resistor increases.
• The temperature of the conductor. As the temperature inreases, resistance increases too.

2.

Wire of uniform cross-section has a resistance of R.
let the diameter be d.
Let the length of the wire be l.
Cross sectional Area be A:

So, Resistance

, here ρ.= Resistivity.
Now a new wire is taken made of the same material,
Let final length be l₁​= 2l, diameter be d₁​= 2d and cross section Area be A₁.

​​

Now, Purring these values of new resistor,

So, New Resitance is R/2.

3.

We know,

where R is resistance l is length of wire A is the cross-section area.

As the question says the resistance is 0.015Ω along its smaller faces implies,

l=5cm=0.05m

A=1×2cm² =0.0002m²

This gives, Resistivity ,

4.

Given :

Resistance R = 28Ω

Using formula, ​, where l is length of wire

A is the cross-section area and, ρ is resistivity of the wire.

To find length l

Solving for l, we get:

5. Diameter d = 10 cm, so, Radius = 5cm = 0.05 m

cross section area, = 0.00785 m^2

length = 1000 m

R = 1.68x10-8 Ω.m ( 1000/0.00785) = 0.00214 Ω. Ans.