Electricity (Class 10): PDF Available to Download

Electricity is the set of physical phenomena associated with the presence and motion of matter that has the property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwell’s equations.

Electric Current  (Charge In Motion)

Definition: The quantity of electric charge flowing through cross-section of a given conductor in one second is called Electric current.

Thus, if Q is the charge which flows through a conductor in time t, then the current (I) is given by

Current{\rm{ }}\left( I \right) = \frac{{Ch\arg e\,(Q)}}{{Time\,(t)}}

The electric current (or current) is a scalar quantity.

Unit of current

The SI unit of charge (Q)  is the coulomb (C), and that of time (t) is second (s). So,

SI unit of current =  \frac{{I\,coulomb}}{{1\sec ond}} = 1 C s–1  =  1 ampere

The unit coulomb per second (Cs–1) is called ampere (A)

Electric Current

The direction of Electric Current

The direction of flow of the positive charge taken as the conventional direction of the electric current.

When we consider the flow of electric current in an ordinary conductor, such as a copper wire, the direction of the current is taken as opposite to the direction of the flow of electrons.

Flow Of Current In A Metal

Metals show a very different kind of bonding called metallic bonding. According to this bonding, the outermost electrons are not bound to any particular atom and move freely inside the metal randomly as shown in fig. So, these electrons are free electrons. These free electrons move freely in all directions. Different electrons move in different directions and at different speeds. So there is no net movement of the electrons in any particular direction. As a result, there is no net flow of current in any particular direction.

Flow of electrons inside a metal wire
The flow of electrons inside a metal wire

Metals show a very different kind of bonding called metallic bonding. According to this bonding, the outermost electrons are not bound to any particular atom and move freely inside the metal randomly as shown in fig. So, these electrons are free electrons. These free electrons move freely in all directions. Different electrons move in different directions and at different speeds. So there is no net movement of the electrons in any particular direction. As a result, there is no net flow of current in any particular direction.

when no potential is applied across its ends

Flow of electrons inside a metal wire
The flow of electrons inside a metal wire

Electric Symbols

Many different kinds of equipment or components are used in setting up electrical circuits. To draw the diagrams of electrical circuits on paper these equipment/components are shown by their symbols. Here are some symbols used in the electric circuit diagrams.

Electric symbol
Electric symbol

Ohm’s Law

Definition: According to Ohm’s law at a constant temperature, the current flowing through a conductor is directly proportional to the potential difference across the conductor.

Thus, if  I is the current flowing through a conductor and V is the potential difference (or voltage) across the conductor, then according to Ohm’s law.

I ∞ V         (when T is constant)

or\,\,I = \frac{V}{R} & .........(i)

where R is a constant called the resistance of the conductor.

Equation (i) may be written as,

V = I × R  ……(ii)

Unit of resistance

The SI unit of resistance (R) is ohm. Ohm is denoted by the Greek letter omega (Ω).

From Ohm’s law,   R = \frac{V}{I}

 

Now, if,            V = 1 volt and I = 1 ampere

Then,\,\,\,\,R = \frac{{1\,volt}}{{1\,ampere}}

Thus, 1 ohm is defined as the resistance of a conductor which allows a current of 1 ampere to flow through it when a potential difference of 1 volt is maintained across it.

Results of Ohm’s law

  • Current flowing through a conductor is directly proportional to the potential difference across the conductor.
Results of Ohm’s law
Results of Ohm’s law
  •  When the potential difference in a circuit is kept constant, the current in inversely proportional to the resistance of the conductor.   I 1/R
  • The ratio of potential difference to the current is constant. The value of the constant is equal to the resistance of the conductor (or resistor). V/I = R

Resistance Of Conductor  

The movement of electrons gives rise to the flow of current through metals. The moving electrons collide with each other as well as with the positive ions present in the metallic conductor. These collisions tend to slow down the speed of the electrons and hence oppose the flow of electric current.

The property of a conductor by virtue of which it opposes the flow of electric current through it is called its resistance.

  •     Resistance is denoted by the letter R.
  •     The SI unit of resistance is the ohm. The ohm is denoted by the Greek letter (W) called omega.
  •      Resistance is a scalar quantity.

Factors on which resistance of a conductor depends

Effect of the length on the resistance of a conductor

The resistance of a conductor is directly proportional to the length. That is the Resistance of a conductor. ∝ Length of the cond.

Effect of the area of cross-section on the resistance of a conductor, The resistance of a conductor is inversely proportional to its area of cross-section.
That is, the Resistance of a conductor

R = \propto \frac{1}{{Area\,of\,cross - \sec tion\,(a)\,of\,the\,conductor}}

* If the area of the cross-section of the conductor is doubled, its resistance gets halved.

  • Effect of temperature on the resistance of a conductor

The resistance of all pure metals increases with a rise in temperature. The resistance of alloys increases very slightly with a rise in temperature. For metal when the temperature increases resistance increases and for semiconductors when the temperature increases resistance decreases.

  • Effect of the nature of the material on the resistance of a conductor

Some materials have low resistance, whereas some others have much higher resistance. In general, an alloy has higher resistance than pure metals which form the alloy.

* Copper, silver, aluminum, etc., have very low resistance.

* Nichrome, constantan, etc., have higher resistance. Nichrome is used for making heating elements of heaters, toasters, electric iron, etc.

Resistivity

\begin{array}{l} R \propto l\\ R \propto \frac{1}{a}\\ So,\,\,R = \frac{l}{a}\\ R = \rho \times \frac{l}{a}........(i) \end{array}

where ρ(rho) is called resistivity of the material of the conductor.

If,             l = 1 m and a = 1 m2

Then          R = ρ                           …(ii)

Thus, if we take a 1-meter long piece of a substance having a cross-sectional area of 1 meter2, then the resistance of that piece of the substance is called its resistivity.

The resistivity of a substance can also be defined as follows :

The resistance offered by a cube of a substance having a side of 1 meter, when current flows perpendicular to the opposite faces, is called its resistivity.

Units of resistivity

From equation (i), we can write

\rho = \frac{{R \times a}}{\ell }

So,{\rm{ }}SI{\rm{ }}unit{\rm{ }}of{\rm{ }}resistivity{\rm{ }}(\rho ){\rm{ }} = \frac{{ohm\, \times \,{m^2}}}{m} = {\rm{ }}ohm.m

Thus, the SI unit of resistivity is the ohm. m (or Ω . m)

Classification of Material on Basis of Resistivity

Substances showing very low resistivities: The substances which show very low resistivities allow the flow of electric current through them. these types of substances are called conductors.

For example, copper, gold, silver, aluminium, and electrolytic solutions are conductors.

Substances having moderate resistivity: The substances which have moderate resistivity offer appreciable resistance to the flow of electric current through them. Therefore, such substances are called resistors. For example, alloys such as nichrome, manganin, constantan and carbon are typical resistors.

Substances having very high resistivity: The substances which have very high resistivities do not allow electricity to flow through them. The substances which do not allow electricity to pass through them are called insulators. For example, rubber, plastics, dry wood, etc. are insulators.

Combination Of Resistances

Series Combination

When two or more resistances are joined end-to-end so that the same current flows through each of them, they are said to be connected in series.

Series Combination
Series Combination

When a series combination of resistance is connected to a battery, the same current (I) flows through each of them.

Law of a combination of resistances in series

The law of combination of resistances in series states that when a number of resistances are connected in series, their equivalent resistance is equal to the sum of the individual resistances. Thus, if R1, R2, R3 …, etc. are combined in series, then the equivalent resistance (R) is given by,

R = R1 + R2 + R3 + …                  ….(i)

Derivation of mathematical expression of resistances in series combination 

Let, R1, R2, and R3 be the resistances connected in series, I will be the current flowing through the circuit, i.e., passing through each resistance, and V1, V2, and V3 be the potential difference across R1, R2, and R3, respectively. Then, from Ohm’s law,

V1 = IR1, V2 = IR2 and V3 = IR3 …(ii)

If, V is the potential difference across the combination of resistances then,

V = V1 + V2 + V3                  …(iii)

If, R is the equivalent resistance of the circuit, then V = IR                                                              …(iv)

Using Eqs. (i) to (iv) we can write,

IR = V = V1 + V2 + V3

= IR1 + IR2 + IR3

or,        IR = I (R1 + R2 + R3)

or,        R = R1 + R2 + R3

Therefore, when resistances are combined in series, the equivalent resistance is higher than each individual resistance.

Some results about the series combination

  1. When two or more resistors are connected in series, the total resistance of the combination is equal to the sum of all the individual resistances.
  2. When two or more resistors are connected in series, the same current flows through each resistor.
  3. When a number of resistors are connected in series, the voltage across the combination (i.e. voltage of the battery in the circuit), is equal to the sum of the voltage drop (or potential difference) across each individual resistor.

Parallel Combination

When two or more resistances are connected between two common points so that the same potential difference is applied across each of them, they are said to be connected in parallel.

Parllel Combination
Parallel Combination

When such a combination of resistance is connected to a battery, all the resistances have the same potential difference across their ends.

Derivation of mathematical expression of parallel combination :

Let, V be the potential difference across the two common points A and B. Then, from Ohm’s law

Current passing through R1,I1 = V/R1    …(i)

Current passing through R2,I2 = V/R2    …(ii)

Current passing through R3,I3 = V/R3     …(iii)

If R is the equivalent resistance, then from Ohm’s law, the total current flowing through the circuit is given by,

I = V/R                            …(iv)

and             I = I1 + I2 + I3                    …(v)

Substituting the values of I,I1,I2 and I3 in Eq. (v),

                                \frac{{\rm{V}}}{{\rm{R}}} = \frac{{\rm{V}}}{{{{\rm{R}}_{\rm{1}}}}} + \frac{{\rm{V}}}{{{{\rm{R}}_{\rm{2}}}}} + \frac{{\rm{V}}}{{{{\rm{R}}_{\rm{3}}}}}...\left( {vi} \right)

Cancelling common V term, one gets

                                \frac{{\rm{1}}}{{\rm{R}}} = \frac{{\rm{1}}}{{{{\rm{R}}_{\rm{1}}}}} + \frac{{\rm{1}}}{{{{\rm{R}}_{\rm{2}}}}} + \frac{{\rm{1}}}{{{{\rm{R}}_{\rm{3}}}}}

The equivalent resistance of a parallel combination of resistance is less than each of all the individual resistances.

Important results about the parallel combination :

(i)    Total current through the circuit is equal to the sum of the currents flowing through it.

(ii) In a parallel combination of resistors the voltage (or potential difference) across each resistor is the same and is equal to the applied voltage i.e. v1 = v2 = v3 = v :

(iii) Current flowing through each resistor is inversely proportional to its resistance, thus the higher the resistance of resistors, the lower will be the current flowing through it.

Read Also: Class 10 Physics Chapter 2 – Magnetic Effect of Current Note

Electricity Class 10 Note: Download Now 

Electricity: Frequently Asked Questions

What is a Simple Definition of Electricity?

Electricity is the set of physical phenomena associated with the presence and motion of matter that has the property of electric charge.

What is Ohm’s Law

According to Ohm’s law at a constant temperature, the current flowing through a conductor is directly proportional to the potential difference across the conductor.

What is electric current and its formula?

The quantity of electric charge flowing through a cross-section of a given conductor in one second is called Electric current.

The formula of electric current

Thus, if Q is the charge which flows through a conductor in time t, then the current (I) is given by

Current{\rm{ }}\left( I \right) = \frac{{Ch\arg e\,(Q)}}{{Time\,(t)}}

What is the conventional direction of electric current? How does it differ from the direction of flow of electrons?

The current flows from the positive terminal to the negative Terminal called the conventional direction of electric current.

What do you mean by elementary charge?

What is the formula for the combination of resistances when they are combined in series and parallel?

Why is the series arrangement not used for domestic circuits?

How does the resistance of a wire vary with its cross-sectional area?

How many electrons pass through a lamp in one minute if the current be 200 mA?