Electrical Resistance and Conductance
Here you can find the complete detail of the theory of electrical resistance and conductance which is useful for competitive exams and science students. We hope you would clear all your concept of electric resistance and conductance from the published post -Complete detail of electrical circuit resistance and conductance. The topic ‘Complete detail of electrical resistance and conductance is written by an expert. The electrical resistance is such a physical quantity that is always unwanted quantity in an electrical circuit but on the other hand, we utilize its great applications in our life.
Electrical resistance and conductance
The electric resistance of any substance is the physical property of a substance that opposes the flow of electric current, It was a German scientist Siemon George Ohm first observe this phenomenon of the matter and discovered Ohm’s law in 8 January 1926. He found the relationship between voltage and current. Conductance is also the physical property of matter which is the ease of flowing electric current means it is the ability of a matter to flow a charge in it.
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Electrical resistance and conductance
Electrical resistance
Ohm’s ‘law states that electric current is directly proportional to the potential difference between the ends of a conductor, the electric resistance is the physical property of the matter which opposes the flow of electric current. The unit of resistance is represented by the last letter (24 th) of Greek alphabet Ω uppercase omega named Ohm after the name of German Physicist George Simon Ohm.
V∝ I
V = IR
Where V is the voltage across a conductor and i is the electric current generated by the voltage across its ends. The electric resistance of conductors like silver, copper, aluminum, and iron is low, three of them, copper, aluminum, and iron are mostly used to build electric wire because silver is not found abundantly in the earth thereby costlier compared to rest of all the metals. All the matters which allow the flow of the electric current is known as the conductors. The resistance of the matter like plastic, air, soil etc is too higher to allow the flow of electric current so these matters are known as insulators.
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The electric resistance in a circuit is required to control the electric current, the resistance of cables and wire is neglected when a net resistance of a circuit is calculated. The components that are used to control electric current are known as resistors,you would have seen the filament of an electric bulb made of spiral tungsten wire, tungsten is used in that because its resistance is higher, this higher resistance causes it to heat up enough to glow. The heating elements in the iron, toaster, electric pan, electric pressure cooker, electric shower, etc are bigger versions of the filaments. Have you observed how a voltage is controlled in a stabilizer or volume of a musical instrument or television, actually in all these cases we increase or decrease the electric resistance through a variable resistor attached with the volume knob.
The resistance of a conductor is directly proportional to the length of the conductors, you can get it through the example of a water pipe, the speed of water is slower in a pipe have more length compared to the pipe of the same radius but of shorter length.The flow of electrons in the wire and the flow of water in the water pipe can be supposed as the same idea.
R ∝ l …..(i)
The resistance of the conductor is inversely proportional to the cross-sectional area of the conductor. You can get it through the example of water flows slower in the thinner pipe compared to the wider pipe if both pipes are of the same length.
R ∝ 1/A
From (i) and (ii) we have
R = ρ. l/A
R= Resistance
l= length of the conductor
ρ = Specific resistance of the matter
It is that’s why the heater wire and tungsten wire is designed into the spiral shape of the coil so as to accommodate its sufficient length in the smaller area of the heater and bulb.
The combination of the resistance- The ways of connecting resistors are of two kinds.(i) Series connections (ii) Parallel connections
(i) Series connections- In the electric circuit when the positive terminal of one resistor is connected to the negative terminal of another resistor then such a combination of resistors is known as the series connections.
The net resistance of the circuit is the sum of magnitudes of all the resistors in series. In series connection, the voltage of the battery is distributed across each resistor in the proportion of their value ,as we know the length is directly proportional to the resistance, so to get the net resistance of the circuit all the individual resistances should be added.
R_{T} = R_{1} + R_{2} + R_{3}
Where R_{T} is the total net resistance of the circuit
The Parallel Connection – When the positive terminal of all the resistors are connected to the positive terminal and the negative terminal of all the resistors are connected to the negative terminal of a battery, then such a combination of the circuit is known as a parallel connection. In parallel connection of resistors, the voltage across each resistor is the same but current drawn by each resistor is in proportion to their magnitude of the resistance.
As we know the resistance is inversely proportional to the area of cross-section of the conductor, hence the net resistance R_{T} of parallel combinations of resistors is calculated as a sum of the reciprocal of their resistance.
1/R_{T} = 1/R_{1} +/R_{2} +R_{3}
R_{T} = (R_{1} R_{2} R_{3} )/(R_{2} R_{3} +R_{3} R_{1} +R_{1} R_{2} )
Electrical resistance and conductance
Conductance
Conductance of the Circuit- The conductance(G)of the circuit is inverse of the resistance
G = 1/R
From Ohm’s law V = iR
R = V/I
G = I/V
The conductance of a substance is the ratio between the electric current and voltage, conductance is the ease with which an electric current passes through a substance, when voltage is constant across an electric component then conductance is directly proportional to the electric current flowing through it.
Unit of conductance is the inverse of Ohm i.e Mho or Siemen, if i =1A and voltage is 1 volt then one unit of conductance is 1 ampere/volt or 1 Mho or 1 Siemen or simply 1S.
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Conductivity
As the conductance is inverse of resistance, on the same way the conductivity is inverse of resistivity.
The conductance of a given material depends on the following physical parameters
The conductance of a substance is inversely proportional to the length of the conductor and directly proportional to the area of the cross-section of the conductor, therefore it can be expressed in terms of the following formula
R = ρ. l/A
ρ = RA/l
σ = 1/ρ
σ = l/RA
R = l/σA
The unit of conductivity is
= (the unit of l)/[unit of R×unit of A)
=m/(Ωm²)
Unit of σ = m/Ωm^{2}
= 1/Ωm = S/m [S=1/Ω,unit of conductance,i.e Siemen)
Unit of conductivity is Siemen/meter
The conductivity of few metals
Metal | Resistivity | Conductivity |
Silver | 1.50×10^{-8} | 6.30×10^{7} |
Copper | 2.44×10^{-8} | 4.10×10^{7} |
Gold | 1.68×10^{-8} | 1.68×10^{7} |
Aluminum | 2.82×10^{-8} | 3.5×10^{7} |
Iron | 1.0×10^{−7} | 1.00×10^{7} |
Calcium | 3.36×10^{−8} | 2.98×10^{7} |
Tungsten | 5.60×10^{−8} | 1.79×10^{7} |
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