# Electrical Resistance

## What is Electrical Resistance?

According to Ohm’s law, there is a relation between the current flowing through a conductor and the potential difference across it. It is given by,

V ∝ I
V = IR

Where,
V is the potential difference measured across the conductor (in volts)
I is the current through the conductor (in amperes)
R is the constant of proportionality called resistance (in ohms)

The electrical resistance of a circuit is defined as the ratio between the voltage applied to the current flowing through it. Rearranging the above relation,

R = $\frac VI$

The unit of electrical resistance is ohms.

1 ohm = $\frac {1~ volt}{ 1 ~ampere}$

Electric charge flows easily through some materials than others. The electrical resistance measures how much the flow of this electric charge is restricted within the circuit.

### Electrical Resistance and Resistivity

So what is resistivity and how can we define resistivity? How is resistivity connected to electrical resistance?

Imagine water flowing through a pipe. The ease of flow of this water will be related to certain things like the cross-section of the pipe, the length of the pipe, even the material of the pipe. Resistance is similar to this. The flowing water is an analogy for flowing charge through a conductor.

Following is the table with related links of resistivity:

### Factors Affecting Electrical Resistance

The electrical resistance of a conductor is dependent on the following factors:

• The cross-sectional area of the conductor
• Length of the conductor
• The material of the conductor
• The temperature of the conducting material

Electrical resistance is directly proportional to length (L) of the conductor and inversely proportional to the cross-sectional area (A). It is given by the following relation.

R = $\frac{ρL}{A}$,

where ρ is the resistivity of the material (measured in Ωm, ohm meter)

Resistivity is a qualitative measurement of a material’s ability to resist flowing electric current. Obviously, insulators will have a higher value of resistivity than that of conductors. The resistivities of a few materials are given below for a comparison. Materials with a low value of resistivity conduct electricity very well.

• Silver – 1.00×10−8
• Copper – 1.68×10−8
• Aluminum – 2.82×10−8
• Wood – 1.00×1014
• Air – 2.30×1016
• Teflon – 1.00×1023

## Resistivity Important Questions

Q1. What is resistivity?

Ans: Resistivity is defined as the magnitude of the electric field across it within a certain current density.

Q2. What is resistivity formula?

Ans: The resistivity formula is given as:

$\rho =\frac{E}{J}$

Where,

• ρ is the resistivity of the material in Ω.m
• R is the electrical resistance of the material in Ω.
• l is the length of the piece of the material in m
• A is the cross-sectional area in m2

Q3. Name the factor that would reduce the resistance through an electric cord.

Ans: As we know that $\rho =\frac{E}{J}$, therefore by increasing the cross-sectional area of the electric cord there will be a reduction in the resistance.

Q4.What happens to the resistivity if resistance and length are constant and the cross-sectional area is doubled?

Ans: As we know that $\rho =\frac{E}{J}$, therefore by solving for resistivity we get,

$\frac{AR}{l}=\rho$

Therefore, resistivity is proportional to the cross-sectional area.

Since A is doubled, keeping resistance and length constant, resistivity will also be doubled.

Q5. How can we decrease the resistance of a wire by a factor of 2?

Ans: As we know that $\rho =\frac{E}{J}$, therefore by doubling the cross-sectional area, resistance can be decreased by a factor of 2.

Q6. What is the unit of resistivity?

Ans: The unit of resistivity is given as Ohm-metre.

Q7. What is the reciprocal of resistivity?

Ans: The reciprocal of resistivity is conductivity.

Q8. What happens to the resistance of pure metals with an increase in temperature?

Ans: As the temperature increases, the resistance of pure metals increase. The reason behind this is the increase in the number of electrons in the conduction band which reduces the mobility thereby increasing the resistance.

Q9. What happens to the resistance of insulators with an increase in temperature?

Ans: As the temperature increases, the resistance of insulators decreases. The reason behind this is the electron movement from the conduction band to the valence band increases as the energy gap between these two bands is large. Therefore, conductance increases and the resistance decreases.

Q10. Name the materials having resistance almost equal to zero.

Ans: Superconductors.

#### Practise This Question

What is the equivalent resistance between A and B in the circuit of figure if R=3 Ω.