Combination of Resistors in Series and Parallel An important part of electric circuits is Resistors. When a resistor connects to a combination of series and parallel connection it forms more complex circuit networks. Regulation of the current level of a device is a resistor’s functionality. To know more about resistors in series or parallel, let’s explore the article further! Introduction Resistors are two-terminal devices. Therefore, voltage division, regulation of current in the device and adjusting signal level are the functionality of a resistor. Representation of a resistor is done through Ohm’s Law. R = V I Many types of resistors are available and some are the following:
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Combination of Resistors in Series and Parallel · Combination of Resistors in Series and Parallel An important part of electric circuits is Resistors. When a resistor connects to
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Combination of Resistors in Series and Parallel
An important part of electric circuits is Resistors. When a resistor
connects to a combination of series and parallel connection it forms
more complex circuit networks. Regulation of the current level of a
device is a resistor’s functionality. To know more about resistors in
series or parallel, let’s explore the article further!
Introduction
Resistors are two-terminal devices. Therefore, voltage division,
regulation of current in the device and adjusting signal level are the
functionality of a resistor. Representation of a resistor is done through
Ohm’s Law.
R =
V
I
Many types of resistors are available and some are the following:
1. Wire-wound resistor.
2. Semi-conductor resistor.
3. Flim resistor.
4. Carbon Composition resistor.
Resistor in Series
In this kind of connection, resistors are in a sequential array of
resistors to form an electronic circuit/ device. Resistors are connected
is in a single line and hence common current flows in the circuit.
The connection is in such a manner that the current flowing through
the 1st register has to then flow further through the 2nd register and
then through 3rd. Therefore, a common current is flowing in
connection with a resistor in series. At all point in the circuit, the
current amoung the resistors is same. For example,
I1 = I2 = I3 = It = 2ma
All the resistors in series that is R1, R2, R3 have current I1, I2, I3
respectively and the current of the circuit is It.
As resistors are connected in series the sum of the individual resistor
is equal to the total resistance of the circuit. Let R1, R2, R3 be the
resistors connected in series and Rt be the total resistance of the
circuit. so the total resistance of the circuit that is 12Ω, is the sum of
all individual resistors R1, R2, R3 having 6KΩ, 4KΩ, 2KΩ
respectively.
This circuit of the resistors in series can also be represented by
Therefore, the total resistance can be calculated as
R1 + R2 + R3 = Rt
furthermore, the total resistance of the above resistors in series is
given by
Rt = 6KΩ + 4KΩ + 2KΩ = 12KΩ
The Equation of Resistors in Series
Since the connection of resistor is in a series fashion that is in the
sequential array or continuously one after other. The total resistance is
equal to the resistance value of each resistor in the device/ circuit.
R1+R2+R3+R4+………………….Rn=Rt
where R is the resistance of the resistor and Rn represents the resistor
number or the total resistance value.
Resistor in Parallel
In this kind of connection, the terminals of resistors are connected to
the same terminal of the other resistor to form an electronic circuit/
device. Resistors are connected is in parallel fashion and hence
common voltage drop in the circuit.
Unlike, series connection, in parallel connection, current can have
multiple paths to flow through the circuit, hence parallel connection is
also current dividers. Common voltage drop is across the parallelly
connected circuits/networks. At the terminals of the circuit, the
voltage drop is always the same. For example
VR1=VR2=VR3=VRT=14V
The voltage across R1 is equal to the voltage across R2 and similarly,
equal to R3 and hence the total voltage drop is equal to the voltage
across the circuit. Reciprocal of individual resistance of each resistor
and the sum of all the reciprocated resistance of resistor will us the
total resistance of the circuit.
1
(
R
t
)
=
1
(
R
1
)
+
1
(
R
2
)
+
1
(
R
3
)
+…………
1
(
R
n
)
Questions For You
Q1: When three identical resistances are connected to form a triangle
the resultant resistance between any two corners is 30Ω .The value of
each resistance is:
1. 90Ω54Ω
2. 15Ω
3. 45Ω
Answer. 45Ω. 1/RAB=1/2R+1/R=2R3=30
RAB=3R/2=3*30/2
⇒R=45Ω
Q2. Identify the changes in a circuit on adding a light bulb in parallel
to the actual resistance of the circuit. It will:
● decrease the total resistance
● increase the total resistance
● make the voltage lost in each light bulb different
● make the current through each light bulb the same
● not change the total current through the circuit
Answer. decrease the total resistance. For a parallel combination of
two resistances,
1/Req=1/R1+1/R2
⟹Req< min {R1, the R2}
A light bulb has its own resistance and hence the total resistance of the
circuit decreases when it is connected in parallel to the actual
resistance of the circuit.
Q3.The least resistance that one can have from six resistors of each 0.1 ohm
resistance is:
1. 0.167 Ω
2. 0.00167 Ω
3. 1.67 Ω
Answer. 1.67 Ω. Least resistance is possible when all are in parallel.
⇒Req=R/6=0.16=0.0167 Ω
Ohm’s Law
Whenever the fan in your room is on and when you feel cold you
reduce the fan’s speed. For doing so you use the speed control knob
on the switchboard. But how does the knob work? What’s its
mechanism? The knob works on the principles of ‘Ohm’s Law’. But
what does Ohm’s law of current electricity state? Let us study Ohm’s
law of current electricity.
Ohm’s Law of Current Electricity
Ohm’s Law of Current Electricity is named after the scientist ”Ohm”.
Most basic components of current electricity are voltage, current, and
resistance. Ohm’s law shows a simple relation between these three
quantities.
Ohm’s law of current electricity states that the current flowing in a
conductor is directly proportional to the potential difference across its
ends provided the physical conditions and temperature of the
conductor remains constant.
Voltage= Current× Resistance
V= I×R
where V= voltage, I= current and R= resistance. The SI unit of
resistance is ohms and is denoted by Ω. In order to establish the
current-voltage relationship, the ratio V / I remains constant for a
given resistance, therefore a graph between the potential difference(V)
and the current (I) must be a straight line.
This law helps us in determining either voltage, current or impedance
or resistance of a linear electric circuit when the other two quantities
are known to us. It also makes power calculation simpler.
Limitations of Ohm’s Law of Current Electricity
● The law is not applicable to unilateral networks. Unilateral
networks allow the current to flow in one direction. Such types
of network consist of elements like a diode, transistor, etc.
● Ohm’s law is also not applicable to non – linear elements.
Non-linear elements are those which do not have current
exactly proportional to the applied voltage that means the
resistance value of those elements changes for different values
of voltage and current. Examples of non – linear elements are
the thyristor.
● The relation between V and I depends on the sign of V. In other
words, if I is the current for a certain V, then reversing the
direction of V keeping its magnitude fixed, does not produce a
current of the same magnitude as I in the opposite direction.
This happens for example in the case of a diode.
How do we find the unknown Values of Resistance?
It is the constant ratio that gives the unknown values of resistance. For
a wire of uniform cross-section, the resistance depends on the length l
and the area of cross-section A. It also depends on the temperature of
the conductor. At a given temperature the resistance,
R =
ρl
A
where ρ is the specific resistance or resistivity and is characteristic of
the material of wire. Using the last equation,
V = I × R =
Iρl
A
I/A is called the current density and is denoted by j. The SI unit of
current density is A/m². So,
E I = j ρ I
This can be written as E = j ρ or j = σ E, where σ is 1/ρ is
conductivity.
Solved Questions for You
Q1. The unit for electric conductivity is
A. per ohm per cm
B. ohm × cm
C. ohm per second
D. who
Solution: A. We know that R =
Iρl
A
. R has dimensions of an ohm, L has dimensions of length A has
dimensions of (length)². Therefore, ρ has dimensions of ohm-cm.
Q2. What will happen to the current passing through a resistance, if
the potential difference across it is doubled and the resistance is
halved?
A. Remains unchanged
B. Becomes double
C. Becomes half
D. It becomes four times.
Solution: A. Using ohm’s law
I =
V
R
I’ =
2V
R/2
so, I’ = 4I
Hence the current becomes four times.
Electrical Energy and Power
Surely you have faced a situation where some important appliance
stops working because the cells run out. What does that mean? That
means the cell is no more able to give current or we can say that it has
no more energy stored. This means that the energy that is the
chemical energy is consumed in the electric circuits. So in order to
find out the amount of energy consumed, we study the electric energy
or electric power.
Electric Energy
To under the concept of electric energy, let us consider a conductor
carrying the current I and potential difference V between the two
endpoints A and B. Let us denoted the electric potential of A and B as
V(A) and V(B). As we know that current is flowing from A to B so
V(A) >V(B) and the potential difference across AB is V = V(A) –
V(B) > 0
NOW, in a time interval Δt, an amount of charge ΔQ is equal to IΔt
moves from point A to B of the circuit and the work was done by the
electric field is equal to the product of V and ΔQ.
Here if the charges in the conductor move without collisions, their
kinetic energy would also change. Conservation of total energy is ΔK
= I V Δt > 0. The amount of energy dissipated as heat in a conductor
in a time interval Δt is,
ΔW = V ΔQ = VI Δt
Electric Power
The rate at which the electric energy enters the portion of the circuit is
called the electrical power input. The rate at which work is done in
bringing the charged particles from one point to another is known as
electric power. It is denoted by P.
The SI unit of power is watt (W). One watt is the power consumed by
the device catting 1A of current when operated at a potential
difference of 1 V.
P = VI
Applying ohms law we can write
P = I² R = V²/R
The above equation is the power loss in a conductor of resistance R
which carries the current I. The application of electrical power is that
it is transmitted from the power stations which later on reaches our
homes and the industrial factories via transmission cables.
Now we know that the transmission of power is very costly. So how
do we minimize the power loss in transmission cables? Let us consider
a device R to which a power is to be delivered via the cables having
resistance Rc. So if V is the voltage across R and current I then,
P = V I
The wires which are connected to the device from the power station
has finite resistance Rc. So, Pc = I² Rc
∴ P² Rc / V²
Hence the power wasted in connecting the wires is inversely
proportional to V². So the resistance Rc of the transmission cable is
considerable.
Solved Questions
Q1. The circuit given below is for the operation of an industrial fan.
The resistance of the fan is 30 ohm. The regulator provided with the
fan is a fixed resistor and a variable resistor in parallel. Under what
value of the variable resistance given, power transferred to the fans
will be maximum? The power source of the fan is a dc source with an
internal resistance of 60 oh.
A. 3 0HM
B. 0
C. ∞
D. 6 ohm
Solution: The correct option is “B”. The power which transfers to the
fan is P = V²/R where R is the total resistance of the circuit. As power
is inversely proportional to total resistance. So for maximum power,
the total resistance should be minimum. Total resistance here is R =
6r/6 +r + 3. r is the variable resistance. R is minimum when r = 0
Q2. An electric heater has a resistance of 150 ohms and can bear a
maximum current of 1 ampere. If we use the heater on 220-volt mains, the
least resistance required in the circuit will be
A. 70 ohms
B. 5 ohms
C. 2.5 ohms
D. 1.4 ohms
Solution: The correct option is “A”. Given that the heater can bear a
maximum current of 1 ampere we need to add a resistance to the
circuit in series with the heater so that current is less or equal to 1
ampere. Let that resistance be R, then (150+ R) × 1 = 220. R = 70
ohm.
Resistivity of Various Materials
You must have had electric shocks! Haven’t you? Did you get the
shock on a plastic wire? It is not possible. You can’t get shocks from
plastic wires. But, why is it so? It is because of a phenomenon that we
will read about in this chapter. We will study about resistivity of
various materials.
What is Resistance?
We know that electric current that flows in a circuit is as similar to the
water flowing through a river. In a river rock, branches and other