Siemens - Unit of Energy Measurement

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Resistance in electricity is analogous to friction in mechanical physics. Due to friction, mechanical energy is lost in the form of heat. Similarly, due to resistance, the electrical energy is lost as heat. The reciprocal of resistance is electrical conductance and is represented by G = 1/R, where G is the electrical conductance and R is the resistance.

Electrical conductance denotes how easily electricity can pass through an electrical component for a given voltage difference. Electrical conductance is the property of a specific electrical element (for example a particular wire) and conductance is closely related to electrical conductivity (which is the property of the material for example silver wire).

The older SI unit of conductance used to be mho which has been replaced by Siemens (S). This article will look into the basics of electrical conductivity, Ohm’s law and discuss what is unit of conductance.

Ohm’s Law

Ohm’s law expresses the relation between voltage (potential difference V), electric current (I), and resistance (R) in mathematical form. A material can obey Ohm’s law if the resistance of the system is a constant i.e. the voltage and current are proportional to each other. As per Ohm’s law:

I = V/R, where I (current in the circuit) is measured in amperes, V (potential difference) is measured in volts, and R (resistance) is measured in ohms. If this ratio of voltage to current remains constant over a wide range of voltages then the conducting material is said to be an “ohmic” material.

Electrical Conductivity

The property of a material that determines how well it can conduct electricity is referred to as its electrical conductivity. Electrical conductivity and resistivity are closely related so first let us understand what is the resistance of an object. 

In a qualitative sense, resistance defines how difficult it is for electricity to pass through a component. In quantitative terms, the resistance between two points is defined as the difference in voltage between the points to carry a unit of current across those points.

When a current of 1 A (ampere) passes through an electric component with a potential difference of 1 V (volts) then the component is said to have a conductance of 1 S (Siemens). 

The equation of electrical conductance is G = I/E, Where G denotes electrical conductance, I is the current in ampere and E is the voltage in volts.

Factors Affecting Electrical Conductivity

Electrical conductivity is determined largely by the number of electrons in the outermost shell of the conducting material. These electrons determine how easily mobile electrons are generated. The number of atoms per unit volume is also a small factor in determining the electrical conductivity of a material. These atoms give an idea about how many electrons would readily move when placed in an electric field. 

like copper and aluminium have high conductivity and are called conductors while materials like rubber and glass have low conductivity and are called electric insulators. There is another special category of materials, for example, germanium and silicon, which are called semiconductors whose conductivity is in between conductors and insulators.

In general, metals have high conductivity and tend to be conductors of electricity since their outermost shell’s electrons can move easily. Non-metals usually have low conductivity.

What is the Unit of Conductance?

A Siemens unit in a direct current (DC) is equivalent to 1 Ampere per volt (reciprocal of resistance in ohms) while in the case of alternating current (AC), the Siemens conductance unit is reciprocal of impedance. If the applied voltage is constant then the current in DC is directly proportional to conductance i.e. if the current is doubled, conductance is also doubled, and similarly, if conductance is cut to 1/5th, current also reduces to 1/5th of its value. The same rule applies to many low-frequency AC systems for example any household utility circuits. But, in some AC circuits with high frequency, the situation gets more complex since some components in these systems store and release energy which is accompanied by dissipation and conversion of energy. Now, since we know what is the unit of conductance, let us take a look at the old units that were used before the use of Siemens.

History of the Unit of Electrical Conductance

The symbol of the unit of conductance was created to depict conductance and it is the capital letter “G”. The unit of conductance was mho (which is ohm spelt backwards, since conductance is the reciprocal of resistance). But in later years, mho was replaced by the unit of Siemens as the SI unit of electrical conductance which is similar to the change in the unit of temperature from Centigrade to Celsius (even the unit of frequency used to be cps (cycles per second) which later changed to Hertz.). You can see a pattern here since Siemens, Hertz, and Celsius are all surnames of famous scientists. 

Conductance and Resistance Relationship

Since conductance is reciprocal of resistance we can figure out that the greater the resistance in a component, the lower would be its electrical conductance (and vice versa). So if there are two components “C1” and “C2” and if the resistance of “C1” is half of that of “C2” then we can easily conclude that “C1” is twice more conductive than “C2”. 

How Conductance is Calculated?

If we know the resistance, voltage, current, conductivity, we can easily calculate the conductance of a specific electrical component. Let us see how we can calculate conductance from the parameters provided.

  • Resistance is known -  If a circuit element has a resistance of 1.2 * 103 ohms, we can find its conductance as G = 1/R = 1/(1.2 * 103) = 0.8 * 103 Siemens. 

  • Voltage and current are known - Let us say in an electric circuit a voltage of 5 volts generates a current of 0.3 amperes in a unit length of wire then from Ohm’s law we know V = I * R or R = V/I. Since G = 1/R, G = I/V = 0.3/5 = 0.06 siemens. 

  • The resistivity of the material and area of cross-section of conducting material is known - The relationship between resistivity and G (conductance) is G = (A * σ)/L, where A is the area of cross-section of the wire and σ is its resistivity. If there is an iron rod whose radius is 0.001 meters and length is 0.1 meters we can calculate the conductance as follows:

    • The value of σ for iron is 1.03 * 107 Siemens/m

    • Area of the rod = 𝛑 * r2 = 𝛑 * 0.0012 = 3.14 * 10-6.

    • Conductance = (1.03 * 107 * 3.14 * 10-6)/0.1 = 324 Siemens

FAQ (Frequently Asked Questions)

Q1. What is Total Parallel Conductance and how do You Calculate it?

Ans1 - When there are circuits connected in parallel, the current inside has multiple pathways or branches to traverse through. This reduces the total resistance of the circuit due to the ease with which current can flow in a parallel circuit having a network of multiple branches. So, additional branches result in lesser resistance and greater conductance. The total parallel conductance in a parallel circuit is more than the conductance of any of the individual branches since parallel resistors work better together than they would separately.

The total conductance is given as, GTotal = G1 + G2 + G3 + G4

Q2. What is Specific Resistance?

Answer - Specific resistance of a material is given by the resistance that a unit length and unit cross-section of material offers to the flow of electricity when a voltage is applied to it. Specific resistance is denoted by the symbol rho (⍴) and the SI unit of specific resistance is Ω-cmil/ft or Ω-meters (metric). The formula for specific resistance is given by R = ⍴ * l/A where R is resistance,  A is the cross-sectional area, and l is the length. From this equation, we can figure out that as the length l of a wire increases, the resistance of the wire also increases. The resistance decreases if the area of the wire increases.