Ohm’s Law

Table of Contents

Ohm’s law is the relation between electric current and potential difference discovered by a school teacher George Simon Ohm of Germany in 1827. It states that “the potential difference across the ends of a conductor is directly proportional to the current flowing through the conductor at constant physical conditions like temperature, dimensions, etc.
Let the current flowing through the conductor be I and the p.d. across the ends of the conductor be V, then, according to Ohm’s law, \[V∝I\] \[V=IR\text{ __(1)}\] Where, the proportionality constant R is called the electrical resistance of the conductor. Its value depends upon the nature, temperature and dimension of the conductor.
The equation (1) is the equation of a straight line passing through origin, y=mx. So, for Ohmic conductor, the graph between p.d. and current is a straight line passing through the origin whose slope gives resistance of the conductor.

Current Voltage Graph for Ohmic Conductors

Ohmic And Non Ohmic Conductors

The conductors which obey Ohm’s law are called Ohmic conductors. All metallic conductors Ag, Al, Cu, Fe etc are Ohmic conductors. CuSO₄ solution is also an Ohmic conductor. The graph between p.d. and current for such conductors is a straight line passing through the origin. 
​The conductors which do not obey Ohm’s law are called Non Ohmic conductors. Examples of such conductors are diode valve, triode valve, transistors, electrolytes (H₂SO₄ solution, AgNO₃ solution, etc). The graph between p.d. and current for such conductors is not a straight line.

Current Voltage Graoh for a Diode

​The relation V/I=R is also valid for non Ohmic conductors. The value of R is constant for Ohmic conductors but not for non Ohmic conductors.

Resistance

​Resistance of a material of a conductor is its property which opposes the flow of charge. \[R=\frac{V}{I}\] For constant potential difference, if resistance increases then current decreases. Hence, resistance of a conductor opposes the conductor. Its circuit symbol is

Symbol of Resistance

​The unit of resistance is volt per ampere (VA⁻¹) which is also called ohm (Ω). Cause of resistance When charge carriers move under the action of applied electric field, then they collide with atoms or molecules of the material and hence their velocity is decreased. This opposition in the motion of the charge carriers is the resistance of the material.

Factors affecting Resistance of a Conductor

1. Nature of the material: Resistance is different for different nature of conductors. The resistance of platinum is 6 times more than that of copper having same length and same cross sectional area.
2. Length: Resistance of a conductor is directly proportional to its length.\[R ∝l\]
3. Area of cross section: Resistance of a conductor is inversely proportional to its cross sectional area. \[R ∝\frac{1}{A}\]
4. Temperature: When a conductor is heated, the free electrons start to collide more with atoms. Due to increase in collisions, resistance of the conductor also increases.
In case of a semiconductor and nonmetal, electrons are not free as in metallic conductor. So, when the conductor is heated, the electrons in the outermost orbit become mobile and their conductivity increases.
​Let R0 be the resistance of the conductor at 0°C and Rθ be its resistance at θ°C. Then, \[R_θ=R_0(1+αθ)\] Where, α is a constant called temperature coefficient of resistance whose value depends upon the nature of the material and slightly on temperature. It is defined as increase in resistance per unit original resistance per unit rise in temperature. Its unit is °C⁻¹. The value of α is positive for metallic conductor, so when for metals, when temperature increases, resistance increases. For semiconductor and nonmetallic conductors, the value of α is negative. Hence, their resistance decreases with increase in conductor.

Electrical Resistivity

​Ohm gave law of resistance as, 
​1. Resistance is directly proportional to the length of the conductor. \[R∝l\text{ __(2)}\] 2. Resistance is inversely proportional to the cross sectional area of the conductor. \[R∝A\text{ __(3)}\] From (2) and (3), \[R ∝\frac{l}{A}\] \[R=ρ\frac{l}{A}\text{ __(4)}\] Where ρ is a constant called resistivity of the material of the conductor whose value depends upon the nature of the material of the conductor and temperature. If l=A=1, then, from (4), \[R=ρ\] Thus, resistivity of a material is defined as the resistance of the material having unit length and unit cross sectional area. Its SI unit is Ωm⁻¹.

Electrical Conductance and Conductivity

The reciprocal of resistance of a conductor is called electrical conductance of the conductor. It is the ease with which the charge carriers flow through the conductor. It is denoted by G. \[Conductance=\frac{1}{Resistance}\] \[G=\frac{1}{R}\] Its SI unit is ohm⁻¹ or mho or Siemens (S). 
​The reciprocal of resistivity of a conductor is called electrical conductivity of the conductor. It is denoted by σ. \[Conductivity=\frac{1}{Resistivity}\] \[σ=\frac{1}{ρ}\] Its SI unit is per ohm per metre (Ω⁻¹m⁻¹) or mho per metre or Siemens per metre.

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