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)

Electrical Resistance

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

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Practise This Question

If the power of two lenses and P1 and P2; when they are combined; the effective power is: