Electrical Resistance and Resistivity

Electrical Resistance

The measure of the opposition to current flow in an electrical circuit is called as Electrical Resistance. In other words we can say that Electrical Resistance measures how the device or material decreases the electric current flowing through it.

Electrical Resistance interrupts the electron movement in the material. Whereas applied potential difference through the conductor boosts the flow of electrons, but resistance do exactly opposite i.e. it decreases the flow of electrons across material. Combination of these two aspects determines the amount by which charge flows among two terminals.

By electrical resistance measurement we can know that;

    1) If there is high resistance, then there will be low current flow.

    2) If there is low resistance, then there will be high current flow.

Let consider two dissimilar types of conductors are placed in a circuit. Here the total current flowing in each conductor are not be the same. The reason behind this are;

    1) The easiness by which electrons in the conductors are capable to travel in the structural arrangement of the conductor material. If the electrons are tightly attached to the crystal lattice structure, then it’s very hard to pull these electrons to make them free, so these electrons float in a particular way. In another conductor material several free electrons wandering arbitrarily nearby the crystal lattice structure. So, this conductor material allows the current to move in very simple way. That’s why copper is mostly used to carry current.

    2) Length also affects the electrical resistance of the conductor. If conductor length is short, the resistance will be less.

    3) Cross sectional area of the conductor is also important reason. The broader the cross sectional area then there is low resistance.

Unit of Resistance

Measuring unit of resistance is ohms (Ω). Symbol of resistance is Greek letter “omega” (Ω). It is named after Georg Simon Ohm.

Resistance Formula

R = V / I

The resistance (R) of an object can be define as, the ratio of voltage (V) across it to current (I) through it.

Resistance is Measured in

Resistance is measured in analog or digital multimeter or ohmmeter. Resistance is the measurement of effort of electrons to flow easily in a conductor or a specific thing. It is like a friction, which a thing undergoes or experience when it is moved on a surface. As you now know that resistance is measured in ohms and as per or considering Ohm’s law; 1 ohm is equivalent to 1 volt of electrical variance per 1 ampere of current i.e. 1Ω = 1V / 1A.

Constant Current (CC) and Constant Voltage (CV) are the two methods, by which electrical resistance is measured.

In the constant current method a known current is applied across an unknown resistance and the generated resultant voltage is measured. For the resistance value below 200 Mega Ohm this method is normally used and digital or analog multimeters are mostly used for this purpose.

In the constant voltage method a known voltage is applied across an unknown resistance and the generated resultant current is measured. For the resistance value more than 200 Mega Ohm this method is normally used. Resistance of this level is generally a leakage measurement, such as; leakage of capacitor, resistance of insulator and isolation contact of relay. Big advantage of this method is in measuring the unidentified resistance with many applied constant test voltages. This will helps to measure the resistance response with several levels of test voltages.

Electrical Resistance and Resistivity

Resistivity

Electrical Resistivity is an important characteristic of a conductor material that measures how intensely that material opposes the electric current flow. It is also called as volume resistivity or exact electrical resistance. A low resistivity of a material specifies that this material easily permits the electric current flow.

Resistivity describes amount of conducting elements in per unit volume of a material. Resistivity also describes amount of charge these conducting elements transmits and how easily they can flow or pass in an electric field.

The electrical resistance (R) of a conducting material rely not only on the material from which the conductor is made but also on its physical dimensions.

The conductor resistance is directly proportional to its length (L) i.e. R ∝ L. So, if we increase its length, there will be increase in its resistance. If we decrease its length there will be decrease in its resistance.

The conductor resistance is inversely proportional to its cross-sectional area (A) i.e. R ∝ 1/A. So, if we increase cross-sectional area there will be decrease in its resistance, and if we decrease its cross-sectional area, there will be increase in its resistance.

The “resistivity factor” which is occasionally called as “specific electrical resistance” permits the resistance of dissimilar conductor types to compare with one another at a specified temperature as per their physical characteristics, ignoring their lengths or cross-sectional areas. So, the greater the resistivity value of ρ, then there will be more resistance and vice versa.

Let consider an example; the resistivity of a good electricity conductor like copper is 1.72 x 10¯⁸ohm-metres, while the resistivity of a poor conductor like an air can be very high or over then 1.3 × 10¹⁶ to 3.3 × 10¹⁶Ω-m at 200°C.

Apart from Copper other example of lower resistive material is Aluminium. Lower resistivity makes easily electric current can flow through it, and hence copper and aluminium is used to make wires.

Below are the factors which affect the resistance of a conductive material;

    1) The resistivity (ρ) of the material by which the conductor is prepared.

    2) The temperature of the conductor.

    3) Conductor’s total length (L).

    4) The conductor’s cross-sectional area (A).

Electrical Resistivity decides that material is a “conductor” or an “insulator” or a “semiconductor”.

In electrical system or power generation system, the earth grounding system is used. Here resistivity is important, as these electrical systems critically depend on the resistivity of the soil material at the place of the system ground.

Resistivity Symbol

Resistivity Symbol is the Greek letter ρ (rho).

Unit of Electrical Resistivity

The Ohm-metre (Ω-m) is the SI unit of electrical resistivity. 

Consider an example; if a solid cube of material size 1m×1m×1m has sheet contacts on two opposite faces, and 1Ω is the resistance among these, then 1Ωm is the resistivity of this material.

Resistivity Formula

The material resistivity is defined in relation to the electric field magnitude across that material, which gives a definite current density. So, Resistivity Formula we can write as;

ρ = E / J

Where;

ρ is the material resistivity in ohm metres (Ω-m)
E is the electric field magnitude in volts per metre (Vm¯¹)
J is the current density magnitude in amperes per square metre (Am¯²)

Most of the conducting materials or resistors have constant cross sectional area with a constant electric current flow. So, more exact and mostly used Resistivity Formula we can write as:

Ρ = R (A / l)

Where:
    R is the electrical resistance of a material having constant size and measured in ohms (Ω)
    l is the material length and measured in metres (m)
    A is the cross-sectional area of the material and measured in square metres (m²)

Resistivity of Materials

Resistivity of Materials is as follows;

• Copper, annealed = 1.72x10¯⁸
• Aluminium = 2.65x10¯⁸
• Silver = 1.59x10¯⁸
• Gold = 2.44x10¯⁸
• Iron = 9.71x10¯⁸
• Platinum = 10.6x10¯⁸
• Lead = 22x10¯⁸
• Mercury = 98x10¯⁸
• Nichrome = 100x10¯⁸
• Tungsten = 5.6x10¯⁸
• Germanium* = 1 to 500x10¯³
• Silicon* = 0.1 to 60
• Carbon* = 3 to 60x10¯⁵
• Hard Rubber = 1 to 100x10¹³
• Glass = 1 to 10000x10⁹

*The semiconductor materials resistivity depends on the occurrence of impurities in the material.

More details on Resitors and how it works you can find in my previous blog;
"Resistor and Working of Resistor".

Conclusion

Electrical Resistance defines the link between current and voltage in a circuit. It depends on the entire number of electrons and how much distance they have to cross i.e. it depends on the length and cross sectional area of the material. Resistivity is a property related to the material where size and shape of material decides the resistance.