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CURRENT ELECTRICITY - I
Salient features:
Definitions
Electric circuits
Series and parallel combination of cells
Electric resistance and Ohm’s law
Series and parallel combination of resistances
Heating effects of electricity, Joule’s law
DEFINITIONS
ELECTRIC CURRENT:
The net charge flowing through a cross section of a conductor in unit time is called
“current”
Current i = q/t
Current is measured in ‘Amperes’. Or Coulomb / Second
AMPERE;
Ampere is an mount of current in a conductor, when the net flow of charge per second
through its cross section is one coulomb.
ELECTRIC POTENTIAL AND POTENTIAL DIFFERENCE
Electric potential at a point in space is defined as the work done in moving a single unit
positive charge from infinity with out any acceleration from infinity to that point.
Potential V = W/q
Potential is measured in “Volt” or Joule/ Coulomb
VOLT
The electric potential difference between two points is said to be one
VOLT, when one joule of
work is done in carrying one coulomb of positive charge from one point to the against the electric field.
ELECTRO MOTIVE FORCE ( e.m.f )
The electromotive force (emf) is defined as the amount of work done by the seat on charge
carriers to force them to go to the point of higher potential.
SIMPLE ELECTRIC CIRCUITS
A simple electric circuit is an arrangement consisting of a source of electrical energy, a
device which utilizes this energy and conducting wires which connect them.
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B Battery (Source of energy)
K Key
L Load (Power consumer)
SERIES AND PARALLEL COMBINATION OF CELLS
SERIES COMBINATION
When a negative terminal of a cell is connected to the positive terminal of the next cell, then
the cells are said to be in “series”
When cells are connected in series, the total emf of the combination is the sum of the emf of
the individual cells.
V = V1 + V2 + ----------
PARALLEL COMBINATION
When all positive terminals of two or more cells are connected to a single point and similarly
all negative terminals are connected to another single point, then the cells are said to be connected in
parallel.
When cells of different emf are connected in parallel the effective emf is equal the emf of that
cell which has the greatest emf.
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When cells of equal emf are connected in parallel the effective emf remains same as that of
any one of the cells.
SOME SYMBOLS USED IN ELECTRIC CIRCUITS
ELECTRIC RESISTANCE AND OHM’S LAW
RESISTANCE:
The electrical property of a conductor by virtue of which opposition is offered to the free
flow of electrons in the conductor is called “Resistance”
Resistance is measured in OHMS (Ω )
The reciprocal of resistance is called as Conductance. C = 1/R
Definition of OHM
The resistance of a conductor is said to be one ohm if a potential difference of one volt
between its ends causes a current of 1 ampere in it.
OHM’S LAW
The electric current (i) in a conductor is directly proportional to the potential difference (V)
between its ends, at a constant temperature (T).
Vαi
V= ir
Magic triangle to remember Ohm’s law
EXPERIMENT TO VERIFY OHM’S LAW
AIM:
1) To verify OHM’s law
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2) To know the resistance of a conductor
APPARATUS:
Battery, Ammeter,volt meter, Rheostat, Unknown resistor, Connecting wires.
Circuit Diagram:
EXPERIMENT:
•
•
Connect the apparatus as shown in the diagram
Adjust the position of the rheostat such that a maximum current flows in the
circuit.
• Then note the readings in the voltmeter and Ammeter.
• Then changing the position of Rheostat gradually repeat the experiment and
take about 6 readings.
• Note down the readings of Voltmeter (V) and Ammeter (i) and tabulate the
readings in the following table.
Volt meter reading V (Volts)
Ammeter reading i (amperes)
V/i = R
S.No
•
•
•
Calculate the ratio of V / i in each case and enter the values in the last column
of the table. This value is almost same.
This value is the resistance of the unknown resistor.
This experiment verifies the OHM’s law.
GRAPH
Draw a graph taking V on x-axis and i on y- axis. This graph will be a straight line.
i
V
Ohmic conductors
The conductors which obey ohm’s law are called ohmic conductors. The V, i graph for these
conductors is a straight line.
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Ex: All metals.
Non Ohmic Conductors:
The devices or conductors which do not obey Ohm’s law are called non-ohmic conductors or
non-linear conductors. The V, i graph for these conductors is not a straight line.
Ex: Semi conductors.
LAWS OF RESISTANCE:
FIRST LAW
The resistance of a conductor is directly proportional to the length of the conductor.
Rαl
SECOND LAW:
The resistance of a conductor is inversely proportional to the area of cross section of the conductor.
R α 1/A
SPECIFIC RESISTANCE:
The specific resistance (ρ) of a material is defined as the resistance of its specimen of unit length and
unit are of cross section.
ρ = RA/l
Specific resistance can be measured in Ohm - meter.
Specific resistances of some metals
METAL
SPECIFIC RESISTANCE
COPPER
STEEL
ALUMINIUM
MANGANIN
(ρ )AT 200C OHM - METER
1.7 x 10-8
18 X 10-8
2.8 X 10-8
44 X 10-8
RESISTANCES IN SERIES AND PARALLEL
SERIES COMBINATION OF RESISTANCES
•
In a circuit, resistors are connected end-to-end are said to be in series, if the same current
exists in all of them through a single path.
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•
•
•
•
•
The voltage across a group of resistors connected in series is equal to the sum of the voltages
across individual resistors.
V = V1 + V2 + V3 + - - - - When resistances are connected in series, their equivalent resistance is equal to the sum of the
individual resistances.
R = R1 + R2 + R3 + - - - - Effective resistance of a series combination is more than that of resistance of any one of
them. This verifies the First law of Resistance.
PARALLEL COMBINATIONOF RESISTANCES
•
In a circuit, resistors are connected to common terminals are said to be in parallel if identical
potential difference exists across all of them.
•
The total current in a circuit containing a group of resistors connected in parallel is equal to
the sum of the currents through individual resistances.
I = I1 + I2 + I3 + - - - - • When resistances are connected in parallel, the reciprocal of their equivalent resistance is
equal to the sum of the reciprocals of the individual resistances.
• 1/R = 1/R1 + 1/R2 + 1/ R3 + - - - - • The effective resistance of a parallel combination is less than that of the resistances of any
one of them. This verifies the second law of reistance.
HEATING EFFECTS OF ELECTRIC CURRENT : JOULE’S LAW
In 1860, Joule conducted a series of experiments and gave the relation between work done
(W) and heat (Q) produced. Hence the heat developed due to conversion of any form of work or energy is
called ‘Joule Heat’. Thus in a resistor, electric current causes heating effect.
When a potential difference is applied between the ends of a metallic conductor, the free
electrons gain energy and begin to drift. In the process, they collide with the ion-core of the conductor and
transfer energy. Then, the ions begin to vibrate with increased amplitude. This results in the increase of
temperature of the conductor which transmits heat to the surroundings. This is called the heating effect of
electric current.
Factors governing heating effects of electric current
1) The quantity of heat produced by a current in a given time is directly
proportional to the
resistance.
QαR
2) The quantity of heat produced by a current in a resistance is directly proportional to the time for
which current flows through it.
Qαt
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3) The quantity of heat produced by a current in a resistance is directly
proportional to the square of the magnitude of the current.
Q α i2
From the above three, we come to know that Q = i2Rt/J
Derivation of Q = i2Rt/J
Electric potential at a point in space is defined as the work done in moving a single unit
positive charge from infinity with out any acceleration from infinity to that point.
Potential V = W/q
→ W = Vq → (1)
From the definition of Current, i = q/t
→ q = it → (2)
There fore, (1) → W = Vit → (3)
According to Ohm’s law, V =iR
Therefore, (3) → W = i2Rt → (4)
According to Joule’s law the amount of heat produced in a conductor is directly proportional to work done.
Wα Q
W = JQ
Q = W/J → (5)
Substituting (4) in (5), we get
Q = i2Rt/ J
ELECTRIC POWER:
Rate of electric work done is defined as electric power.
Electric power P = W / t.
Units of Electric power are Joule / Second (or) Watt.
WATTAGE OF ELECTRICAL APPLIANCES
Wattage of
an electrical appliance is defined as the rate at which electrical energy is consumed by
it.
1 Kilo Watt Hour = 1000 Watts
1 Mega Watt = 106 Watts.
HOUSE HOLD CONSUMPTION OF ELECTRICAL ENERGY
The units of household consumption of electrical energy are Kilo Watt Hours (KWH)
Watt Hour is defined as the electrical energy consumed by an appliance of 1 Watt for an hour.
1 Watt hour = 1 Watt x 1 Hour
= 1 Watt x
60 x 60 Seconds
= 3600 Watt – seconds.
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1 KWH = 1000 Watt Hours.
= 1000 x 3600 Watt Seconds
= 36 x 105 Watt seconds
1 Unit = 1 KWH
HOME APPLIANCES USING HEATING EFFECTS OF ELECTRCITY
Electric stove, Soldering rod, Electrical Fuse, Immersion Heater, Iron box, Electrical Heater, etc. are the
household appliances using heating effects of electricity.
IMPORTANT QUESTIONS:
4 MARKS
1.
2.
3.
4.
State Ohm’s law? Describe an experiment to verify Ohm’s law?
(March-05, 01)
Show that the effective resistance of a series combination in a circuit is equal to sum their
resistances? (or) Derive R = R1 + R2 + - - - (June -06, Mar-06, 04)
Show that the reciprocal of the effective resistance of a parallel combination in a circuit is
equal to the sum of their reciprocals? (or)
(Apr-08, Jun - 07, Mar – 02)
Derive 1/R = 1/R1 + 1/R2 + - - - 2
(Mar-08, Jun-02)
State Joule’s law and derive Q = i Rt / J?
2 MARKS
1.
2.
3.
What are Ohmic and Non Ohmic conductors? Give Examples? (Jun-01)
State the laws of Resistances?(Mar-07)
Derive W = i2Rt?
1 MARK
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Define electric current?
Define Ampere?
What do you mean by Potential Difference?
What is electromotive Force (emf) of a cell?
What is a simple electric circuit?
When do you say that the cells are connected in Series?
When do you say that the cells are connected in parallel?
When three cells of emf’s 1V, 1.5V, and 2V are connected in parallel, What is the effective
emf of the combination?
Define electrical resistance of a conductor?
Define the term OHM? (Mar-05)
State Ohm’s law?
The P.D across a bulb is 240V and a current of 3A flows through it. Find the resistance of the
bulb?
On what factors does the resistance of a conductor depend?
Define Specific resistance (or) Resistivity of a conductor?
What is electric power?
What do you understand by the term wattage of an electric appliance?
State Joule’s law?
(June-03,02,01)
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18.
19.
What is the difference between Galvanometer, and Ammeter? (Mar-00)
Calculate the equivalent resistance of two resistors of 100Ω and 1Ω connected in parallel?
(Jun-02)
BITS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Unit of Electric current - - -- - - -----(Mar-99)
The Potential Difference between two terminals can be measured by ____
(Jun-07)
Units of electrical charge ---------------Symbol of Battery ------------------------ (Mar-03, Jun-06)
---------------- is used to measure the flow of current in a circuit.(Mar-00)
The effective resistance when two resistors of 8 Ω are connected in parallel is -----------------(Mar-08)
The effective resistance when two resistances of 6 Ω and 12 Ω are connected in series is ---------------------(Mar-03)
Unit of Specific resistance is --------------------(Mar-03,01)
A 1.5 V battery is connected such that a current of 0.15A flows through the circuit. Then the
resistance of the conductor is ------------- (Jun-05)
Substances or conductors which do not obey Ohm’s law are known as --(Mar-06, Jun-02)
Unit of Electrical power --------------The formula used to find current is -------------The nature of a substance to oppose the flow of current is known as its -----The symbol of Resistance is -----------------The effective resistance is less than any individual resistances when resistances are connected in -------------ANSWERS FOR BITS
1) Ampere
2) Volt meter 3) Coulomb
4)
5) Ammeter
7) 18 Ω 8) Ohm – meter 9) 10Ω 10) Non ohmic conductors 11) Watt
12) i = q/t
13) Resistance 14)
15) Parallel.
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6) 4 Ω