# EMF and Ohm’s Law

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### Electric Current Through Conductor: • A conductor is made up of very minute particles called as atoms. Atoms consist of a positively charged nucleus and negatively charged electrons which move around the nucleus in different orbits.
• The electrons in the last orbit are loosely attached to the atoms. They can be removed by applying external force, hence such electrons are called as free electrons.
• If one end of the conductor is connected to positive terminal of a battery and another end is connected to negative terminal of a battery, negatively charged free electrons start moving towards the positive terminal of battery Thus there is a flow of electron through the conductor and we can say that electric current is flowing through the conductor.
• Actually, electrons flow from negative terminal of a battery to positive terminal of a battery through the external circuit. But conventionally it is assumed that electric current flows from positive terminal to the negative terminal of a battery.
• If ‘e’ is a charge on one electron and ‘Q’ is a total charge flowing through the conductor, then t6he number of electrons (n) flowing through the conductor can be found by using the relation Q = n e.

#### Conductors:

• The substances which allow electric current to flow through them easily are called good conductors of electricity.
• In conductor electric current flows due to free electrons.
• e.g. All metals. Silver, Aluminium, Copper etc.

#### Insulators:

• The substances which do not allow electric current to flow through them are called bad conductors or insulators of electricity.
• e.g. Plastic, Rubber, Glass etc.
• Rubber plastic, wood don’t have the free electrons in them, hence they do not allow the electric current to pass through them. Such materials are called as insulators or bad conductors.

#### Electric Current:

• The rate of flow of charge with respect to time through given cross-section of the conductor is called an electric current. The symbol of current is ‘I’. The unit of current is ampere (A)

I = q/t

Where I    =   electric current

t    =   time

q   =   electric charge

#### A Potential Difference Across the End of Conductor is Required For the Flow of Electrons:

• A conductor contains free electrons, which are in random motion i.e. they move in any possible direction with any possible velocity. Due to which the number of electrons passing in unit time through any section of the conductor in one direction is equal to the number of electrons passing in unit time through that section in the opposite direction. Therefore, the net flow of change is equal to zero. Therefore, no current flows through the conductor.
• When a potential difference is applied across the conductor the negatively charged electrons start moving towards the positive end of the conductor. Thus electrons start moving in the definite direction. Thus current flows through the conductor. Hence we can conclude that for a flow of electrons in a conductor, the potential difference across the end of the conductor is required.

#### Cause of a Resistance of a Conductor:

• A metallic conductor consists of a large number of free electrons. These electrons are always in a state of random motion. When a potential difference is applied across the ends of the conductor. These free electrons start moving in the definite direction i.e. towards the positive end of the conductor.
• During this process, the electrons flow through the crowd of vibrating atoms. These electrons collide with the atoms. Thus vibrating atoms offer obstruction to the flow of electrons. This obstruction to the flow of electrons is called as the resistance of the conductor.
• If the temperature of the conductor is increased, the kinetic energy of vibrating atoms is increased, due to which the atoms start vibrating with higher amplitude. Thus the obstruction to the flow of electrons increases and hence the resistance of the conductor also increases.

#### Resistance of Wire:

• Experimentally it is found that the value of resistance (R) depends on length (L) of a conductor, area of cross-section (A)  of conductor and nature of a conductor as follows :

The resistance is directly proportional to the length of a conductor.

R ∝  L   …………..  (1)

The resistance is inversely proportional to the area of a cross-section.

R ∝  1/A   …………..  (2)

The resistance depends on nature of conductor.

From equation (1) & (2) ρ is constant called specific resistance or resistivity.

This is an expression for the resistance of a conducting wire This is an expression for the specific resistance or the resistivity of a material of a conductor.

#### Resistivity or Specific Resistance:

We have, Let A = 1 unit  and L = 1 unit

∴ R    = ρ

• Thus specific resistance or resistivity of a material of a conductor is defined as that resistance of a conductor whose area of cross section and its length is unity.

#### Unit of Resistivity: Therefore, unit of resistivity or coefficient of resistance is  ohm metre (Ωm)

#### Conductance:

• Reciprocal of resistance is called as conductance (K). Its unit is mho or siemens (S).

K = 1 / R

#### Conductivity:

• Reciprocal of resistivity is called as conductivity (k). Its S.I. unit is siemens per metre (S/m)

k = 1/ρ

#### Notes:

• Resistivity is a measure of opposition to the flow of electric current, while conductivity is a measure of assistance to the flow of electric current i.e. easiness of flow of electric current.
• A material exhibiting high resistivity has low conductivity, while material exhibiting high resistivity has low conductivity.

#### Copper wires are generally used as connecting leads in an electrical circuit.

• Copper has an extremely small specific resistance, hence the resistance of a conductor made up of copper is very less. Thus there is a very small loss of electrical energy when a current flows through a copper wire.
• Due to its high conductivity, a thin copper wire can be used. Hence, copper wires are used for to save energy and cost.

#### Coils of electric iron are made up of nichrome.

• Electric-iron works on the principle of the heating effect of electric current. Hence in electric iron more heat is to be produced. When the value of resistance of the coil is more, the more heat is generated.
• Nichrome is alloy whose specific resistivity is very high. Hence resistance or coil made from nichrome possesses higher resistance. Hence coils of electric iron are made up of nichrome.

#### The resistance coils in high-quality resistance boxes are made of manganin.

• Resistance box is used in electrical experiments. Resistance box contains a number of resistances of different values. These values should remain constant even if there is a change in room temperature.
• Manganin has a very small temperature coefficient of resistance and therefore for a small change in temperature, the change in the resistance of a manganin coil is negligible. Hence the value of resistance made from manganin remains constant.
• Hence the resistance coils in high-quality resistance boxes are made of manganin.

### Ohm’s  Law:

• Statement: Physical conditions of the conductor (i.e. the length, area of cross-section, the material and the temperature) remain the same, the potential difference across the terminal of the conductor is directly proportional to the electric current flowing through the conductor.
• Explanation :

Let ‘V’ be the potential difference across the conductor and ‘I’ be the current through it, then by ohm’s law

V  ∝   I

V   =   R I

Where R = constant called resistance of the conductor.

#### Graphical Representation of Ohm’s Law

• For conductors obeying ohm’s law we get straight line. The resistances obeying ohm’s law are called as ohmic resistances or linear resistances. #### Note:

• For some conductors, we don’t get straight lines but we get curves as shown below.  • From above graphs, we can conclude that these resistances are not obeying ohm’s law that’s why they are called as non- ohmic or non-linear resistance.

### Temperature Dependence of Resistance:

• A metallic conductor consists of a large number of free electrons. These electrons are always in a state of random motion. When a potential difference is applied across the ends of the conductor. These free electrons start moving in the definite direction i.e. towards the positive end of the conductor.
• During this process, the electrons flow through the crowd of vibrating atoms. These electrons collide with the atoms. Thus vibrating atoms offer obstruction to the flow of electrons. This obstruction to the flow of electrons is called as the resistance of the conductor.
• If the temperature of the conductor is increased, the kinetic energy of vibrating atoms is increased, due to which the atoms start vibrating with higher amplitude. Thus the obstruction to the flow of electrons increases and hence the resistance of the conductor also increases.

#### Expression for Temperature Coefficient of Resistance:

Let Ro be the initial resistance at 0° C  Let R be the resistance at t° C.

∴  Change in resistance             =    R  –  Ro

∴  Change in temperature (Δt)   =    t2  – t1

Experimentally it is found that the change in resistance

is directly proportional to the original resistance.

R  –  Ro   ∝    R      ——— (1)

is directly proportional to change in temperature.

R  –  Ro   ∝    t2  – t1  ——— (2)

From (1) & (2)

R  –  Ro    ∝   R (t2  – t1)

R  –  Ro    =      α Ro (t2  – t1)

Where α  is constant called  temperature coefficient of resistance.

But    t2  – t1 =  Δ t

R  –  Ro    =      α Ro  Δ t    ……….. (3)

R   =    Ro  +  α Ro  Δ t

R   =    Ro  ( 1 + α Δ t )

This is an expression which gives the value of resistance at the new temperature.

From equation (3), we have This is an expression for the temperature coefficient of the resistance of a material of a conductor.

#### Temperature Coefficient of Resistance:

• Temperature coefficient of resistance is defined as the change in resistance per unit resistance at 0° C per degree rise in temperature

#### Notes:

• For good conductors value of temperature coefficient of resistance is positive hence value of resistance increases as temperature increases and value of resistance decreases if its temperature decreases
• For semiconductors value of temperature coefficient of resistance has negative value. Hence the value of resistance decreases as temperature increases and value of resistance decreases if its temperature increases.

#### Thermistors: • A thermistor is a special case of a semiconductor having a large negative temperature coefficient of resistance. Thermistors are also called as temperature sensitive resistance.
• As they have a large negative value of alpha the value of resistance decreases very fast, as the temperature increases. Thermistors are very sensitive.
• Thermistors are made up of oxides of copper, manganese, nickel, cobalt, iron, lithium etc. These oxides are mixed and are powdered. After this, they are given desired shape and are heated to very high temperature. Thus ceramic thermistors are formed.
• Thermistors are used in the temperature controlling devices or as temperature sensors.
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