Introduction

- Electricity is a branch of physics which deals with the nature and effects of stationary or moving electric charges. Electricity is the most convenient and widely used form of energy. This energy can be transmitted over long distance with relatively small loss in energy. In India, several power plants like Thermal Power Plant, Hydro Electric Power Plant, Nuclear Power plant,
*etc.,*are constructed for generating large amount of electricity. The fundamental concepts of electricity such as electric charges, their properties, resistance, potential difference, electric power, energy, electric current, effects of current and their various applications in day to day life are discussed below.

**Electric Charges**

There are two kinds of electric charges. The electric charge developed by rubbing a glass rod with silk is different from the charge developed by rubbing an ebonite rod with fur. The electric charge developed on glass rod was calledViterous, while the charge developed on ebonite rod was called Resinous. Benjamin Franklin (American scientist) who introduced the modern concept of electric charges. He named Viterous as positive charge and Resinous as negative charge.

**Properties of Electric Charges:**

The important properties of electric charges are as follows:

(i) Electric charge is a scalar quantity.

(ii) The magnitude of negative or positive charge is same and is equal to 1.6 × 10–19 C.

(iii) Like charges repel, while unlike charges attract each other.

(iv) Electric charge is always conserved, *i.e.,* charge can neither be created nor destroyed.

**SI unit of charge: **The SI unit of charge is coulomb. It is denoted by C. 1 coulomb of charge is equivalent to the charge of nearly 6 × 1018 electrons.

**Static (or Frictional) Electricity:** The electric charges developed on objects when they are rubbed with each other is called frictional electricity.

Frictional electricity is also called static electricity because charges so developed cannot move from one part of the object to the other part.

**Current Electricity: **The electricity produced due to the movement of charges is called current electricity.

**Conductors: **Those substances through which electricity can flow freely are called conductors.

*For Example***: **Silver, copper, aluminium, graphite, etc.

**Insulators: **Those substances through which electricity cannot flow are called insulators.

*For Example***: **Glass, rubber, paper, plastic, *etc*.

## Electric Current

The amount of charge flowing through a given cross-section of a conductor per unit time is called electric current.

Let Q be the amount of charge flows through a conductor in time *t* seconds, then electric current is given by

Electric current is a scalar quantity. The SI unit of electric current is ampere (A).

1 ampere =

or 1 A = 1 Cs–1

Thus, electric current flowing through a conductor is said to be 1 ampere when 1 coulomb charge flows through any cross-section of a conductor in 1 second.

Smaller units of electric current are:

1 milli-ampere (mA) = 10–3 A

1 micro-ampere (µA) = 10–6 A

**Note: **How many electrons are in 1 coulomb of charge?

We know, Q = *ne *where *n* is the number of electrons.

or= 6.25 × 1018 electrons

1 coulomb of charge contains nearly 6 × 1018 electrons.

Direction of Electric Current

Conventionally, the direction of electric current in an electric circuit is opposite to the direction of flow of electrons, *i.e.,* the direction of current is from positive terminal of a cell (or battery) to the negative terminal, through external circuit.

**Electric Circuit: **

A continuous and closed path of an electric current is called an electric circuit. Electric circuits are represented by drawing circuit diagrams.

A simple electric circuit is shown in the figure.

**Open Circuit: **An electric circuit through which no electric current flows is known as open electric circuit.

**Closed Circuit:** An electric circuit through which electric current flows continuously is known as closed circuit.

*Note***:** *Ammeter is an instrument used to measure the electric current through a branch of circuits. An ammeter is always connected in series in an electric circuit. This is because the resistance of ammeter is very small so that it does not affect the effective resistance of the circuit.*

Electric Potential and Potential Difference

The electrostatic potential at any point in the electric field is defined as the work done in bringing a unit positive charge from infinity to that point. Potential is denoted by the symbol V and its SI unit is volt.

The potential difference between two points in an electric field is defined as the amount of work done in moving a unit positive charge from one point to the other. That is,

Potential difference (V) between two points =

or

When, W = 1 joule and Q = 1 columb then, V = = 1 JC–1

or 1 volt = 1 JC–1

Thus, the potential difference between two points is said to be 1 volt if 1 joule of work is done in moving 1 coulomb of electric charge from one point to another.

Potential difference is a scalar quantity and it is measured by means of an instrument called voltmeter. The voltmeter is always connected in parallel across the points between which the potential difference is to be measured.

Circuit Diagram

An electric circuit comprises a cell (or a battery), a plug key, electrical component (s) and connecting wires. It is often convenient to draw a schematic diagram in which different components of the circuit are represented by the symbols conveniently used. The various electrical symbols used in electric circuits are given in the following table.

S. No. | Components | Symbols |

1. | An electric cell | |

2. | A battery or a combination of cells | |

3. | Plug key or switch (open) | |

4. | Plug key or switch (closed) | |

5. | A wire joint | |

6. | Wires crossing without joining | |

7. | Electric bulb | or |

8. | A resistor of resistance R | |

9. | Variable resistance or rheostat | or |

10. | Ammeter | |

11. | Voltmeter |

Ohm’s Law

Ohm’s Law gives a relationship between current and potential difference. Ohm’s law states that at constant physical condition, the current flowing through a conductor is directly proportional to the potential difference across its ends. Thus, according to Ohm’s law,

I µV

or I = V/R

or

where R is a constant of proportionality called resistance of the conductor. The SI unit of resistance is ohm (W).

Graph between V and I is a straight line passing through origin as shown in the figure.

Resistance of a Conductor

The property of a conductor due to which it opposes the flow of current through it is called resistance. The resistance of a conductor is numerically equal to the ratio of potential difference across its ends to the current flowing through it, *i.e.,*

Resistance =

or R =

Now, when V = 1 volt and I = 1 ampere, then

R(1W)= = 1 VA–1 or 1W = 1 VA–1

Thus, 1Wis the resistance of a conductor if the potential difference across its ends is 1 V and the current through it is 1 A.

Factors on which Resistance of a Conductor Depends

The resistance of a conductor depends on the following factors:

(i) Length of the conductor

(ii) Area of cross-section of the conductor (or thickness of the conductor)

(iii) Nature of the material of the conductor

(iv) Temperature of the conductor.

**Effect of Length of the Conductor:** The resistance of a conductor is directly proportional to its length, *ie.,*

R µ*l* …(i) where *l* is the length of the conductor.

Thus, when the length of the conductor is doubled, its resistance also gets doubled and if the length of the conductor is halved, then its resistance also gets halved. That is why a long wire has more resistance and a short wire has less resistance.

**Effect of Area of cross-section of the conductor:** The resistance of a conductor is inversely proportional to its area of cross-section. That is,

R µ …(ii)

where A is the area of cross-section of the conductor. Thus, when the area of cross-section of a conductor is doubled, its resistance gets halved and if the area of cross-section of a conductor is halved, then its resistance will get doubled.

From relation (i) and (ii), we have

R µ

or ….(iii)

Where,r(rho) is a constant known as resistivity (or specific resistance) of the material of the conductor. The SI unit of resistivity is ohm-metre(W m).

Now in relation (iii), if we put A = 1, and *l* = 1 we get

r= R

Thus, the resistivity of material of conductor is defined as the resistance of the conductor of unit length and unit area of cross-section.

*Note***:** *The resistivity of a substance does not depend on its length or thickness. It depends only on the nature and temperature of the substance.*

**Electrical resistivities of some substances at 20°C are given in the following table:**

** Material Resistivity (****W**** m)**

**Conductors** Silver 1.60 × 10–8

Copper 1.62 × 10–8

Aluminium 2.63 × 10–8

Tungsten 5.20 × 10–8

Nickel 6.84 × 10–8

Iron 10.0 × 10–8

Chromium 12.9 × 10–8

Mercury 94.0 × 10–8

Manganese 1.84 × 10–6

**Alloys** Constantan (alloy of Cu and Ni) 49 × 10–6

Manganin (alloy of Cu, Mn and Ni) 44 × 10–6

Nichrome (alloy of Ni, Cr, Mn and Fe) 100 × 10–6

**Insulators** Glass 1010 – 1014

Hard rubber 1013 – 1016

Ebonite 1015 – 1017

Diamond 1012 – 1013

Paper (dry) 1012

From the above table we find that

**Resistivity of Metal < Resistivity of alloys < Resistivity of Insulators**

Thus, the metals and alloys have very low resistivity in the range of 10–8 to 10–6Wm. They are good conductors of electricity.

For example, copper and aluminium metals are generally used for electrical transmission lines. Tungsten metal is used almost exclusively for filaments of electric bulbs. This is because tungsten has high melting point and does not oxidise (or burn) easily at high temperatures.

The resistivity of alloys is generally higher than that of its constituent metals. Also alloys do not oxide readily at high temperature.

For example, Manganin (alloy of copper, manganese and nickel) and constantan (alloy of copper and nickel) are used to make resistors (resistance wires) used in electrical appliances.

Nichrome (an alloy of nickel, chromium, iron and manganese) is used for making the heating elements of electrical appliances like electric iron, room heaters, toaster, immersion rod, etc.

*Note***: ***The resistivity of semi-conductors like silicon and germanium is in between those of conductors and insulators and decreases on increasing the temperature.*

Combination of Resistances (or Resistors)

There are two methods of joining the resistors together (i) in series and (ii) in parallel.

**Resistors in Series **

When two (or more) resistances are connected end to end consecutively, they are said to be connected in series.

Let three resistances R1, R2 and R3 are connected in series which is shown in the figure.

or

or

Thus, their equivalent or effective resistance is given by

Rs = R1 + R2 + R3

In a series combination of resistors, the current (I) is the same in every part of the circuit or same current will flow through each resistor. But the potential difference V is equal to the sum of potential difference across the individual resistors.

*i**.e.,* V = V1 + V2 + V3

Now, suppose that the total resistance of the combination be Rs and the current flowing through the whole circuit be I, then

V = RI

Since, the same current I flows through resistances R1, R2 and R3 connected in series, so by applying Ohm’s law to the resistances separately we get,

IRs = IR1 + IR2 + IR3

or

Thus, we conclude that when several resistors are joined in series, the resistance of the combination Rs equals to the sum of their individual resistances.

Resistors in Parallel

When two (or more) resistances are connected between the same two points, they are said to be connected in parallel.

Let us consider the arrangement of three resistors joined in parallel as shown in the figure.

or

In parallel combination of resistors, the potential difference across each resistance is equal to voltage of the battery (or cell) applied. But the total current (I) is equal to the sum of the separate currents through each branch of the combination.

Let V be the applied potential difference across A and B. The current I drawn from the battery divides into three parts I1, I2 and I3 at point A as shown in the figure.

I = I1 + I2 + I3

Now applying Ohm’s law to the whole circuit and also to each resistance separately, we get

or

Thus we conclude that the reciprocal of the combined resistance of a group of resistances connected in parallel is equal to the sum of the reciprocals of all the individual resistances.

*Note***: ** *When a number of resistances are connected in parallel, then their combined or equivalent resistance is always less than the smallest individual resistance.*

Advantages of Connecting Electrical Appliances in Parallel

- i) In a series combination, when one component fails, the circuit is broken and none of the components in the circuit works. But in parallel combination if one component fails, the working of other components will not be affected.
- ii) In a series circuit the current is constant throughout the electric circuit. So, it is impracticable to connect electric bulb and an electric heater in series, because they need currents of different values to operate properly. On the other hand, a parallel circuit divides the currents through the electrical gadgets and this is helpful when each gadget has different resistance and requires different current to operate properly.

Electric Power

The rate at which electric energy is dissipated (or consumed) is called electric power. The electric power P is given by

or

The SI unit of electric power is watt (W)

1 watt = 1 = Js–1

Thus, the power is said to be 1 watt when an electrical appliance consumes electrical energy at the rate of 1 joule per second.

Other units of electric power used for commercial purposes are kilowatt and megawatt.

1 kilowatt (1kW) = 103 W

1 megawatt (1 MW) = 106 W

Formula for Calculating Electric Power

As we known that …(i)

Also, the amount of work done when Q charge moves against a potential difference V is

W = Q × V

or W = I × *t* × V …(ii) [Q I = ]

From (i) and (ii), we have

or P = V × I …(iii)

or Electric power = Potential difference × Current

Also, We can write

P = VI

or P = I2R [QV = RI]

or P = [QI = ]

Now, if we put, V = 1 volt and I = 1 ampere in equation (iii), we get electric power of 1 watt.

*i.e.*, Power = 1 watt = 1 volt × 1 ampere

or 1 watt = 1 VA

Thus, the power consumed by an electrical appliance is said to be 1 watt when

1 ampere of current is operated at a potential difference of 1 volt.

Electric Energy

We know that Electric power =

Now, according to law of conservation of energy,

work done by electric current = Electric energy consumed

\ Power, P =

or W = P × *t*

* *or E = P × *t*.

Commercial Unit of Electrical Energy

For commercial purpose we use a bigger unit of electrical energy which is called kilowatt-hour (kWh).

One kilowatt-hour is the amount of electrical energy consumed when an electrical appliance having a power rating of 1 kilowatt is used for 1 hour.

1 kWh = 1000 W × 60 × 60 seconds

= 1000 joules/seconds × 3600 seconds

= 3600000 joules

= 3.6 × 106 J

Heating Effect of Electric Current

Whenever the electric current is passed through a metallic conductor, it becomes hot after some time. This indicates that the electrical energy is being converted into heat energy. This effect is known as heating effect of current.

Cause of Heating Effect of Current

When a potential difference is applied across the ends of a conductor, an electric field is set up across its ends. A large number of free electrons present in the conductor get accelerated towards the positive end and acquire kinetic energy due to which an electric current flows through the conductor. These accelerated electrons on their way suffer frequent collisions with the ions or atoms of the conductor and transfer their gained kinetic energy to them. As a result of this, the average kinetic energy of vibration of the ions or atoms of the conductor rises and consequently the temperature of the conductor rises. Thus the conductor gets heated due to the flow of electric current through it.

Heat Produced in a Conductor

Consider a conductor AB connected to cell as shown in the figure. Let V be the potential difference applied across the ends of AB and I be the current flowing through AB in time *t*.

Now, by definition of potential difference

Work done in carrying the charge Q from A to B is

W = V × Q

= V I *t* [ Q = I *t*]

= I2R*t* [ V = R I]

This work done is equal to the heat (H) produced in the conductor.

*i.e.,* H = I2 R *t*

or H = *t*

Applications of Heating Effect of Current

- i) The heating effect of current is used in electrical heating appliances like electric iron, room heater, toaster, electric kettle, electric oven,
*etc*. All these heating appliances contain coils of high resistance wire made of nichrome alloy. - ii) The heating effect of electric current is utilized in electric bulbs for producing light. Here the filament must retain as much of the heat generated as is possible, so that it gets very hot and emits light. It must not melt at such high temperature. A strong metal with high melting point such as tungsten (about 3380°C) is used for making bulb filaments. The filament should be thermally isolated as much as possible using insulting support etc. The bulbs are usually filled with chemically inactive nitrogen and argon gases to prolong the life of filament.

iii) An electric fuse is safety device connected in series with the electric circuit. A fuse wire is generally prepared from copper or tin-lead alloy whose melting point is very low. When the current in a domestic electric circuit rises too much, the fuse wire gets heated, melts and breaks the circuit, thereby prevents the fire and damage to various electrical appliances.

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solved examples |

**Example 1:** The circuit shown in the figure is the two resistances are connected in series.

=

(a) If R1 = 6 W and R2 = 3W, what is the equivalent resistance RT ?

(b) If R1 = 0.08 W and R2 = 0.17 W, what is the value of RT ?

(c) If R1 = 0.5 W and R2 = 0.2 W, what is the value of RT ?

(d) If the equivalent resistance is measured to be RT = 27 W and it is known that R2 = 15 W, what must the value of R1 be?

(e) If R1 = 2 W and R2 = 3W, and a current of 3A is measured to flow through them, what is the potential difference across each of the individual resistors and what is the total potential difference?

**Solution:** (a) RT = R1 + R2 = 6W + 3W = 9 W.

(b) RT = R1 + R2 = 0.08 W + 0.17W = 0.25 W.

(c) RT = R1 + R2= 0.5W + 0.2 W = 0.7 W

(d) R1 = RT – R2 = 27 W – 15 W = 12 W.

(e) RT = R1 + R2= 2W + 3W = 5 W.

Given, I = 3 A

Applying ohm’s law, we get V1 = IR1 = 6 V.

V2 = IR2 = 9 V.

**Example 2:**

Find the equivalent resistance (in W) for the circuit shown above.

**Solution:**

Note that the 4 and 5 are NOT in parallel because the 2 and 8 are in between. The 1 and 2 are NOT in series because the 4 is in between. The 1 and 7 are NOT in parallel because the 4 is in between. The only combination you can make (at first) is the 3, 6 and 9 are in series, so:

Now the 5 and 18 are in parallel

The 2, 3.9, and 8 are in series: The 4 and 13.9 are in parallel

Finally, all three are in series \ RT = 1 + (4|| {2 + [5|| (3+ 6 + 9)] + 8}) + 7 = 11.1 W

**Example 3:**

Find the equivalent resistance of the circuit network shown above.

**Solution:** The 2W and the 4W are shorted out. Another way to think about it is that the 2W and 4W are in series, forming a 6W resistor. However, the 6W is in parallel with the wire (*a* wire is 0W). Which is

0 || 6W = 0 6W/(0 + 6W) = 0

Then we have the other two resistors in series, so

RT = 3W + 0 + 5W = 8W

**Example 4:** 1 W and a 2 W resistor are connected in parallel and this pair of resistors is connected in series with a 4W resistor. What is the equivalent resistance of the whole combination? What is the current flowing through the 4 W resistor if the whole combination is connected across the terminals of a 6 V battery (of negligible internal resistance)? Likewise, what are the currents flowing through the 1W and 2 W resistors?

**Solution:** The equivalent resistance of the 1W and 2 W resistors is

giving RT* = *0.667 W. When a 0.667 W resistor is combined in series with a 4W resistor, the equivalent resistance is RT = 0.667 + 4 = 4.667 W.

The current driven by the 6 V battery is

This is the current flowing through the 4 W resistor, since one end of this resistor is connected directly to the battery with no intermediate junction points.

The voltage drop across the 4 W resistor is

V4 = IR4 = (1.24) (4) = 5.14 V

Thus, the voltage drop across the 1W and 3 W combination is V11 = 6 – 6.14 = 0.857 V. The current flowing through the 1W resistor is given by

Likewise, the curent flowing through the 1W resistor is

Note that the total current flowing through the 1W and 3 W combination is I11= I1 +I2=1.19 Å, which is the same as the current flowing through the 4 W resistor. This make sense because the 1W and 3 W combination is connected in series with the 4 W resistor.

**Example 5:** An electric refrigerator rated 400 W operates 8 hour/day. What is the cost of the energy to operate it for 30 days at Rs. 3.00 per kWh?

**Solution:** The total energy consumed by the refrigerator in 30 days would be 400 W × 8.0 hour/day

× 30 days = 96000 Wh = 96 kWh

Thus the cost of energy to operate the refrigerator for 30 days is 96 kWh × Rs. 3.00 per kWh = Rs. 288.00.

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EXERCISE |

- A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R´, then, find the ratio of R/R´
- Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. Find the ratio of heat produced in series and parallel combinations.
- A copper wire has diameter 0.5 mm and resistivity of 1. 6 × 10–8W m. What will be the length of this wire to make its resistance 10 W? How much does the resistance change if the diameter is doubled?
- A battery of 9 V is connected in series with resistors of 0.2 W, 0.3 W, 0.4W, 0.5W and 12 W respectively. How much current would flow through the 12 W resistor?
- How many 176 W resistors (in parallel) are required to carry 5 A on a 220 V line?
- Show how you would connect three resistors, each of resistance 6 W so that the combination has a resistance of (i) 9 W, (ii) 4 W.
- Compare the power used in the 2W resistor in each of the following circuits: (i) a 6 V battery in series with 1 W and 2W resistors, and (ii) a 4 V battery in parallel with 12 W and 2 W resistors.
- Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is 220 V?
- Since matter is made of electrically charged particles, why don’t we and the objects around us feel electric forces all the time?
- An atom loses its two outermost electrons. How does the resulting ion behave when it is near a positively charged transparency? A negatively charged tissue? Would anything be different if it lost only one electron?
- The current in a wire is one ampere. Explain this statement in terms of the charge flowing through the wire.
- Calculate the work done in taking a charge of 0.02 C from A to B if the potential at A is 20 V, and that at B is 30 V.
- A current of 1.5 A flows through a wire of resistance 8 W. Find the amount of heat produced in

10 seconds. - Find
- a) the equivalent resistance,
- b) the current passing through the cell
- c) the current passing through the 30-W resistor in the circuit shown in the figure.

** **

- Find the current supplied by the cell in the circuit shown in the figure.
- Two students perform the experiments on series

and parallel combinations of two given resistors R1 and R2 and plot the following V-I graphs.

Which of the graph is (are) correctly labelled in terms of the words “series” and “parallel”. Justify your answer.

- Two metallic wires A and B are connected in parallel. Wire A has length
*l*and radius*r*, wire B has a length 2*l*and radius 2*r*. Compute the ratio of the total resistance of parallel combination and the resistance of wire A. - You are given three resistors of 10W, 10W and 20W, a battery of emf 2.5V, a key, an ammeter and a voltmeter. Draw a circuit diagram showing the correct connections of given components such that the voltmeter gives a reading of 2.0 V
- A student assembled a circuit as shown here. He noted readings of voltmeter V and ammeter A by adjusting the rheostat Rh. The readings recorded by him were.

** **Which of the observation is wrong and why?

- Describe a simple experiment to demonstrate variation of resistance on (i) length, (ii) cross-section area, and (iii) material of the conductor. What are the conclusions drawn?

WORKSHEET – 1

** **

- Inth
- A Ca

(a)

- A dis
- A gro
- is

(a)

WORKSHEET – 2

WORKSHEET – 3

- At
- Aa
- M
- At
- W

(a

(c

WORKSHEET – 4

- Ac
- Au(ab
- Ac
- Aa
- Tdc

** **

WORKSHEET – 5

- C
- C
- AF
- In

(a

(b

(c

(d

- Ath

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