# 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.

### 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