In
a closed electrical circuit the sum of the potential drops is equal to the sum
of the potential raises.
PROBLEM
– 01
Three
lamps A, B and C takes 0.7, 0.8 and 0.9 amps respectively. When they are
connected across 110 V supply. Calculate the value of current when they are
connected in series across 220 V supply. Assuming filament resistances to remain
unaltered. Find the voltage across each lamp.
PROBLEM
– 02
Four
resistors and two voltage sources are connected as shown in figure. Find the
voltage drop across each resistance.
PROBLEM
– 03
Six
resistors and one voltage source are connected as shown in figure. Find the
current flow through the one ohm resistor and verify Kirchhoff’s voltage law.
PROBLEM
– 04
Seven
resistors and one voltage source are connected as shown in figure. Voltage
across Vab is zero. Find the value of X and verify Kirchhoff’s voltage law.
PROBLEM
– 05
A
60 W, 220 V bulb and 200 W, 220 V bulb are connected in series across a 440 V DC
supply. (i) Find voltage across each bulb and (ii) Determine the value R3 to be
connected in parallel with a 60 W bulb to ensure equal sharing of voltage.
Leon Charles Thevenin was born in Paris on March 30th 1857.
He graduated from the Ecole Polytechnique in 1876 and two years later
joined the Corps of Telegraph Engineers. Appointed as a teaching inspector at
the École supérieure de télégraphie in 1882, he was interested in the problems
of measurement in electrical circuits. As a result of studying Kirchhoff's
circuit laws and Ohm's law, he developed his famous theorem, Thévenin's
theorem, which made it possible to calculate currents in more complex
electrical circuits and allowing people to reduce complex circuits into simpler
circuits, called Thévenin's equivalent circuits. His Theorem was published in
three separate scientific journals in 1883 in a paper entitled "Extension
of Ohm's Law to complex electrical circuits". Three more articles followed
in that year. The first gave a method of using a galvanometer to measure
potential, and made use of the new theorem. The second described a method for
measuring resistance, and the third was on the use of the Wheatstone Bridge.
He was described as a humble man, a model engineer and a kind hearted
person. He died on 21st September 1926 in Paris. He lived for 69
years on this planet and even today he lives in every basic electrical and
electronics textbooks.
THEVENIN’S THEOREM
Any linear active
bilateral network can be replaced by an equivalent circuit consisting of
voltage source in series with a resistance. The voltage source is open circuit
voltage across the open circuited load terminals and the resistance being the
internal resistance of the source network looking from the open circuited load
terminals.
[OR]
Any
two terminal linear network, containing independent voltage and current
sources, may be replaced by a constant voltage source VTH
in series with a resistance RTH where VTH
is the open circuit voltage between the terminals and RTH is the
resistance of the network as seen from the two terminal with all sources
replaced by their internal resistances.
APPLICATIONS
1. This theorem is extensively
used in networks to determine the current through any element or voltage across
any element in a network without rigorous calculation for solving a set of
network equations.
2. It is useful in
circuit analysis when it necessary to find the current only in one branch of a
circuit.
3. It is also useful
when it is necessary to study the variation in the current in a branch of the
circuit when the resistances of this branch is varied.
A
theorem is a result that can be proven to be true from a set of axioms. The
term theorem is used especially in mathematics where the axioms are those of
mathematical logic.
DIFFERENCE
BETWEEN AXIOM AND PROVERB
Axiom
is a statement or proposition which is regarded as being established, accepted,
or self-evidently true.
Proverb
is a short, well-known pithy saying, stating a general truth or piece of
advice.
SUPERPOSITION
THEOREM
In
a circuit having more than one voltage or current source, the total voltage or
total current in any branch is the algebraic sum of voltages or currents in
that branch produced by each source acting separately.
[OR]
When
a number of voltage or current sources are acting in a linear network
simultaneously, the resultant voltage or current in any branch of the circuit
is the algebraic sum of voltages or currents flowing through it taking one
source at a time while deactivating the other sources.
The
voltage source is replaced by its internal resistance while the current source
is replaced by open circuit. If a source is not ideal, it is replaced by its
resistance.
LIMITATIONS
Superposition
principle is applicable only when the source and load have a linear
relationship.
Voltage
and current have a linear relationship (provided the resistances are linear)
and can be found by using this theorem.
“Voltage
and power” and “current and power” are not linearly related. Hence this theorem
cannot be used to find power.
APPLICATIONS
This
theorem is applicable to many systems in electric fields, fluid mechanics,
mechanical engineering, electrical circuit analysis etc.
In 1845, a German
physicist, Gustav Kirchhoff developed a pair or set of rules or laws which deal
with the conservation of current and energy within Electrical Circuits.
KIRCHHOFF’S CURRENT LAW
This law states that the “Total
current or charge entering a junction or node is exactly equal to the charge
leaving the node as it has no other place to go except to leave, as no charge
is lost within the node”.
In other words the algebraic sum
of all the currents entering and leaving a node must be equal to zero,I(exiting) + I(entering) = 0.
The filament of a 220 V metal-filament lamp is to
be constructed from a wire having a diameter of 0.02 mm and a resistivity at 20
degree centigrade of 5 µΏ-cm. If α = 0.005 per degree centigrade, what length
of filament is necessary if the lamp is to dissipate 100 watts at a filament
temperature of 2000 degree centigrade.
PROBLEM
– 02
Find
the current flowing at the instant of switching on a 40 W lamp filament on to a
220 V circuit, if the filament temperature at normal operating condition is
2800 degree centigrade. Resistance temperature coefficient of the filament at
room temperature of 20 degree centigrade = 0.005 per degree centigrade.
PROBLEM
– 03
A copper conductor has
its specific resistance of 1.6 x 10^-6 Ώ-cm at 0 degree centigrade and a
resistance temperature coefficient 39.3 x 10^-4 per degree centigrade at 20
degree centigrade. Find (i) the specific resistance (ii) the
resistance-temperature coefficient at 80 degree centigrade.
PROBLEM
– 04
The resistance
temperature co-efficient for a certain copper wire is 0.004 and for carbon
filament it is 0.0003. How many ohms of carbon filament is series with a 80 ohm
copper wire will make the total combined resistance invariant with temperature.
PROBLEM
– 05
Two
conductors one of copper and other of Iron are connected in parallel. At 20
degree centigrade, they carry equal currents.
If
the temperature is raised to 180 degree centigrade, what is the proportion of
the total current will each conductor carry?
