There are three types of electrical charges: positive charges consist of protons, negative charges consist of electrons, and the SI unit of charge is the coulomb. Conductors contain free or loosely bound electrons that allow them to conduct electricity, while insulators do not have free electrons and obstruct electricity flow. Potential difference is defined as the work required to move a unit positive charge between two points in an electric field. Common measuring instruments include the voltmeter, which measures potential difference, and the ammeter, which measures electric current in amperes. Resistors can be connected in series, where the total resistance is the sum of individual resistances, or parallel, where the total resistance is lower than the lowest individual resistance.

2. Types of charges
• There are two types of charges :-
• Positive charge :- These are made of sub atomic particle
proton.
• Negative charge :- These are made of negative sub atomic
particle electron.

3. S.I. unit of charge
• The S.I. unit of charge is coulomb.
• An electron posses a negative charge of 1.5 x 10-19.
• The S.I. unit of one coulomb is equivalent to the charge
containing 6.25 x 10-18.

4. Conductors and Insulators
Conductors
• These substance have the
property to conduct electricity
through them.
• These have free or loosely held
electrons which helps in
conducting electricity.
• Example – copper.
Insulators
• These substance have the property
to obstruct the flow of electricity.
• These do not have free electrons
present in them.
• Example – Rubber Insulation.

5. Electric potential
• When a small electric charge is placed in the electric field
due to another charge, it experiences a force. So, work has
to be done on the positive charge to move it against this
force of repulsion.
• The electric potential is defined as the work done in
moving a unit positive charge fro infinity to that point.

6. Potential Difference
• The concept of electric potential is closely linked to that of the
electric field. A small charge placed within an electric field
experiences a force, and to have brought that charge to that
point against the force requires work. The electric potential at
any point is defined as the energy required to bring a unit test
charge from an infinite distance slowly to that point.
• It is usually measured in volts, and one volt is the potential
for which one joule of work must be expended to bring a
charge of one coulomb from infinity.

7. Potential difference =
𝑤𝑜𝑟𝑘 𝑑𝑜𝑛𝑒
𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑜𝑓 𝑐ℎ𝑎𝑟𝑔𝑒 𝑚𝑜𝑣𝑒𝑑
.
or, V =
𝑊
𝑄
.
where W = work done.
and Q = quantity of charge moved.
S.I. unit of potential difference is volt.
thus 1 volt =
1 𝑗𝑜𝑢𝑙𝑒
1 𝑐𝑜𝑢𝑙𝑜𝑚𝑏
.

8. Voltmeter
• A voltmeter is an instrument
used for measuring electrical
potential difference between
two points in an electric
circuit.
• Voltmeter has a high
resistance so that it takes
negligible current.

9. Electric Current
• The movement of electric charge is known as an electric
current, the intensity of which is usually measured
in amperes. Current can consist of any moving charged
particles; most commonly these are electrons, but any
charge in motion constitutes a current.
• 1 ampere =
1 𝐶𝑜𝑢𝑙𝑜𝑚𝑏
1 𝑆𝑒𝑐𝑜𝑛𝑑
.

10. Ammeter
• An ammeter is a measuring
instrument used to measure
the electric current in a circuit.
Electric currents are measured
in amperes (A), hence the name.
• An ammeter should have a very
low resistance so that it may not
change the value of current
flowing in the circuit.

11. Circuit Diagram
• We know that an electric circuit, as shown in Fig. 12.1,
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.
Conventional symbols used to represent some of the most
commonly used electrical components.

13. Georg Ohm
• Georg Simon Ohm (16 March 1789 – 6
July 1854) was a German physicist and
mathematician. As a school teacher, Ohm
began his research with the
new electrochemical cell, invented by
Italian scientist Alessandro Volta. Using
equipment of his own creation, Ohm
found that there is a direct proportionality
between the potential difference (voltage)
applied across a conductor and the
resultant electric current. This
relationship is known as Ohm's law.

14. Ohm’s Law
• Ohm’s Law explains the relationship between voltage (V
or E), current (I) and resistance (R)
• Used by electricians, automotive technicians, stereo
installers.
• According to Ohm’s law : At constant temperature, the
current flowing through a conductor is directly
proportional to the potential difference across its end.

15. • According to Ohm’s law:
V ∝ I
or, V= R x I.
where R is constant “resistance” of the conductor.
This can also be written as –
or, I =
𝑉
𝑅
.
So, Current, I =
𝑉
𝑅
.
Therefore,
i. The current is directly proportional to potential difference.
ii. The current is inversely proportional to resistance.

16. Resistance
• An electron traveling through the wires and loads of the
external circuit encounters resistance. Resistance is the
hindrance to the flow of charge. For an electron, the journey
from terminal to terminal is not a direct route. Rather, it is a
zigzag path that results from countless collisions with fixed
atoms within the conducting material. The electrons encounter
resistance - a hindrance to their movement.
• The S.I. unit of resistance is ohm’s (Ω).

17. Factors affecting Resistance
i. Length of conductor.
ii. Area of cross section of the conductor (or thickness of
the conductor).
iii. Nature of the material of the conductor, and
iv. Temperature of conductor.

18. Resistivity
• It has been found by experiments that :
• The resistivity of a given of a given conductor is directly proportional
to its length.
R ∝ l ……………..(1)
• The resistivity of a given conductor is inversely proportional to its
area of cross section.
R ∝ 1/A …………… (2)
Combining (1) and (2), we get :
R ∝ l/A
R =𝑝 ×
𝑙
𝐴
………………….(3)

19. • Where p(rho) is a constant known as resistivity of the material.
• The resistivity of a substance is numerically equal to the resistance of
a rod of that substance which is 1 meter long and 1 square meter in
cross section.
• Resistivity, p =
𝑅 𝑥 𝐴
𝑙
.
• The unit of resistance R is ohm.
• The unit of area of cross-section A is (meter)2.
• The unit of length l is meter.
putting these unit in the above equation –
p =
𝑜ℎ𝑚 × 𝑚𝑒𝑡𝑒𝑟 2
𝑚𝑒𝑡𝑒𝑟
.
p = ohm-meter.
The S.I. unit of resistivity is ohm-meter (Ωm)

20. Resistivity of some common substances (200 C )

21. • The resistivity of alloys are much more than those of pure
metals (from which they are made).
• For example the resistivity of maganine (which is an
alloy of copper, manganese and nickel)is about 25 times
more than that of copper.
• Alloys are used in making heating a materials as –
i. Alloys have very high resistivity (due to which heating
elements produce a lot of heat on passing current).
ii. Alloys do not undergo oxidation easily even at high
temprature.

22. Combination of Resistors
• Resistors can be combined in two ways –
i. In series.
ii.In parallel.

23. Resistors in Series
• When two (or more) resistors are connected end to end
consecutively, they are said to be connected in series.
• According to the law of combination of resistance in
series: The combined resistance of any number of
resistances connected in series is equal to the sum of
the individual resistances.
R= R1 +R2 +R3+………..

24. I. When a number of resistors connected in series are
joined to the terminal of a battery, then each resistance
has a different potential difference across its ends
(which depends on the value of resistance). But the total
potential difference across all the ends of all the resistors
in series is equal.
II. When a number of resistors are connected in series, then
the same current flows through each resistance.

25. Resultant of Resistances connected in
Series
• The figure shows three resistances R1,R2,R3 connected in series. Now suppose
potential difference across resistance R1 is V1 , R2 is V2 and R3 is V3. Let
potential difference across battery be V, then :
V = V1+V2+V3.
Applying Ohm’s law to the whole circuit : V = IR. ………..(1)
Applying Ohm’s law to the three resistors separately, we get:
V1 = I x R1. ………………….. (2)
V2 = I x R2. ………………….. (3)
V3 = I x R3. ………………….. (4)
Substituting (2), (3), (4) in (1)
IR = IR1 + IR2+ IR3
OR, IR= I (R1+R2+R3)
Or, R = R1+R2+R3 .
Therefore we conclude that the sum total resistance in a series resistance
connection is equal to the sum of all the resistances.

26. Resistors in Parallel
• When two (or more) resistors are connected between the same
points, they are said to be connected in parallel.
• According to the law of combination of resistance in parallel:
The reciprocal of the combined resistance of any number
of resistances connected in parallel is equal to the sum of
the reciprocals of the individual resistances.
1/R= 1/R1 +1/R2 +1/R3+………..
• When a number of resistances are connected in parallel then
their combined resistance is less than the smallest individual
resistance.

27. • When a number of resistance are connected in parallel, then the
potential difference across each resistance is same which is equal
to the voltage of battery applied.
• When a number of resistances connected in parallel are joined to
the two terminals of a battery, then different amounts of current
flow through each resistance (which depend on the value of
resistance). But the current flowing through each parallel
resistance, taken together, is equal to the current flowing in the
circuit as a whole. Thus, when a number of resistance are
connected in parallel, then the sum of current flowing through all
the resistances is equal to the total current flowing in the circuit.

28. Resultant of Resistances connected in
Parallel
• The figure shows three resistances R1,R2,R3 connected in series. Now suppose
currant across resistance R1 is I1 , R2 is I2 and R3 is I3. Let total current in the
circuit be I, then:
I = I1+I2+I3.
Applying Ohm’s law to the whole circuit : I = V/R. ………..(1)
Applying Ohm’s law to the three resistors separately, we get:
I1 = V / R1. ………………….. (2)
I2 = V / R2. ………………….. (3)
I3 = V / R3. ………………….. (4)
Substituting (2), (3), (4) in (1)
V/R = V/R1 + V/R2+ V/R3
OR, V/R= I (1/R1 +1/R2 + 1/R3)
Or, 1/R = 1/R1+1/R2+1/R3 .
Therefore we conclude that the sum total resistance in a parallel resistance
connection is equal to the sum of reciprocal of all the resistances.

29. Parallel and Series connection
Parallel connection
• If one electric appliance stops working due
to some defect, then all other appliances
keep working normally.
• In parallel circuits, each electric appliance
has its own switch due to which it can be
turned on or off independently.
• Each appliance gets same voltage as that
of power source.
• Overall resistance of household circuit is
reduced due to which the current from
power supply is high.
Series connection
• If one electric appliance stop working due
to some defect, then all other appliances
stop working.
• All the electric appliances have only one
switch due to which they cannot be turned
on or off separately.
• In series circuit, the appliances do not get
same voltage (220 V) as that of the power
supply line.
• In series circuit the overall resistance of
the circuit increases due to which the
current from the power source is low.

30. Heating effect of electric current
• When electricity passes through a high resistance wire like
a nichrome wire, the resistance wire becomes very hot and
produces heat. This is called the heating effect of current.

31. James Prescott Joule
James Prescott Joule (24 December 1818 – 11 October
1889) was an English physicist and brewer, born in Salford,
Lancashire. Joule studied the nature of heat, and discovered
its relationship to mechanical work. This led to the law of
conservation of energy, and this led to the development of
the first law of thermodynamics. The SI derived unit of
energy, the joule, is named for James Joule. He worked
with Lord Kelvin to develop the absolute scale
of temperature. Joule also made observations of
magnetostriction, and he found the relationship between
the current through a resistor and the heat dissipated, which
is now called Joule's first law.

32. Joule’s law of heating
Let
An electric current I is flowing through a resistor having resistance equal to R.
The potential difference through the resistor is equal to V.
The charge Q flows through the circuit for the time t.
Thus, work done in moving of charge Q of potential difference V = VQ
Since, this charge Q flows through the circuit for time t,

33. • The heat produced in wire is directly proportional to
i. Square of current.
ii. Resistance of wire.
iii. Time for which current is passed.

34. Applications of heating effect of electric
current
There are many practical uses of heating effect of current. Some of the most common are as follows.
• An incandescent light bulb glows when the filament is heated by heating effect of current, so hot
that it glows white with thermal radiation (also called blackbody radiation).
• Electric stoves and other electric heaters usually work by heating effect of current.
• Soldering irons and cartridge heaters are very often heated by heating effect of current.
• Electric fuses rely on the fact that if enough current flows, enough heat will be generated to melt
the fuse wire.
• Electronic cigarettes usually work by heating effect of current, vaporizing propylene glycol and
vegetable glycerin.
• Thermistors and resistance thermometers are resistors whose resistance changes when the
temperature changes. These are sometimes used in conjunction with heating effect of current(also
called self-heating in this context): If a large current is running through the nonlinear resistor, the
resistor's temperature rises and therefore its resistance changes. Therefore, these components can be
used in a circuit-protection role similar to fuses, or for feedback in circuits, or for many other
purposes. In general, self-heating can turn a resistor into a nonlinear and hysteretic circuit element.

35. Electric Energy
• H = I2 Rt gives the rate at which electric energy is dissipated or consumed in an electric
circuit. This is also termed as electric power. The power P is given by
P = VI
Or P = I2R = V2/R
• The SI unit of electric power is watt (W). It is the power consumed by a device that carries 1
A of current when operated at a potential difference of 1 V. Thus,
1 W = 1 volt × 1 ampere = 1 V A
• The unit ‘watt’ is very small. Therefore, in actual practice we use a much larger unit called
‘kilowatt’. It is equal to 1000 watts. Since electrical energy is the product of power and time,
the unit of electric energy is, therefore, watt hour (W h). One watt hour is the energy
consumed when 1 watt of power is used for 1 hour. The commercial unit of electric energy is
kilowatt hour (kW h), commonly known as ‘unit’.
1 kW h = 1000 watt × 3600 second
= 3.6 × 106 watt second
= 3.6 × 106 joule (J)