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Laws of Resistance
1. The resistance
of a conductor varies directly as its length.
2. The
resistance of a conductor varies inversely to its cross section area.
3. The
resistance of a conductor depends on the material.
4. The resistance
of a conductor depends on its temperature.
The above factors can be summed up
mathematically as :
where ρ is
constant representing the nature of material and is known as specific
resistance.
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Effect
of Temperature on Resistance
(a) Resistance of
pure metals and alloys increases with rise in temperature.
(b) Resistance of
electrolytes, insulators and semiconductors decreases with rise in
temperature.
If Ro = Conductor resistance at 0˚C
Rt
= Conductor resistance at t˚C
t = rise in temperature
and αo
= Temperature coefficient of resistance at 0˚C,
Then Rt =
Ro (1 + αot)
The
temperature coefficient at 0˚C is defined at the change in
resistance per ohm for a rise in temperature of 1˚C from 0˚C.
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Grouping
of Cells
A
single cell has an e.m.f. of about 1.5
volts. If either more voltage is needed or more current is required,
then cells are connected either in series or in parallel
respectively. This arrangement of connection is named as grouping of
cells.
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Cells
in Series
When cell are
connected in series, e.m.f. of the battery
is equal to the sum of the e.m.f. of cells.
Internal resistance of battery =sum of internal
resistance of cells.
e.m.f. of battery E =ne
where e is e.m.f. of the cell and n refers to the number of
cells in series.
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Cells in Parallel
The cells when arranged in parallel have
the same e.m.f., but internal resistance of
the unit is reduced.
If n cells are connected in parallel, each of e.m.f.
E,
then
e.m.f. of
the battery = e.m.f. of one cell = E
where
r is the resistance of one cell
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Cells in Series and in Parallel
n = number of cells in each row
m = number of parallel rows.
N = total number of cells = mn.
Let
e.m.f of one cell
=e
E.M.F.
of battery =ne volts
Internal
resistance of each row =nr ohms
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Cell Efficiency
The efficiency of a Cell is considered in two ways:
(1) Ampere-hour (A.h) efficiency.
(2) Watt-hour (W.h.) efficiency.
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D.C. Motors
D.C. motors are classified according to the method of
excitation. They may be of the shunt, series or compound types.
Series Motor
The speed of a series motor is given by the relation:
Shunt motor
where
Ra is the armature resistance. Since  is practically
constant at all loads, speed is there almost constant.
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Types of Armature Winding
The two main types of winding are:
-
Lap
Winding. It is also known as parallel winding or multiple
winding. In this type of winding, the numbers of parallel paths (A)
are equal to the number of poles (P).
-
Wave
Winding. In this case the armature conductors are divided into
two parallel irrespective of the number of poles.
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Slip
The rotor of
induction motor rotates at somewhat lesser speed than the synchronous
speed and actual speed is known as slip.
where Nr is rotor or actual while N is
synchronous speed.
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AC through Resistance and Inductance
In the resistance part of the
circuit the current is in phase with the voltage, while in the
inductive part it is 90˚ out of phase. Hence, to determine the
current, the effect of resistance and reactance has to be combined which
is named as impedance:
where
 is
the phase angle between the voltage and current and cos is
called the power factor.
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Circuits
Containing Resistance, Inductance and Capacitance
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Transformer
Transformer is a device for transferring energy from one
alternating current circuit to another without any change in
frequency. It changes voltage from high to low and low to high with a
corresponding increase or decrease in current. If the voltage is
increased, the transfer is said to be stepped up. If it is decreased,
then it is referred as step down.
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Three Phase Transformer
Whenever the supply is three phase
and it is desired to transform current at another voltage, then
either a single three phase transformer or three separate single
phase transformers can be used. However, in practice a single three
phase transformer is used. The three phase
winding of a transformer can be connected either in star or in delta.
Current
and voltage in star
The e.m.f. between
any line and the neutral gives the phase voltage while the e.m.f. between two outer terminals is known as
line voltage.
Current
in each line is the same as phase current
i.e. Line current IL=Phase
current IP
Line Voltage and Current in Delta
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