Networks and Circuits
Interconnection of some elements is an electrical circuit. A circuit is a network. So to
differentiate between a circuit and a network, we should understand the path of circuit.
A branch represents a single element such as voltage source or a current source or a
resistor.
We can say that a branch is two terminals of an element. The circuit figure shows 5 branches
in the circuit. There is two sources one 20V voltage source, one 4A current source, three
resistors. As the circuit contains five elements so it has five branches. Every element has two
terminals also.
A node is the point of connection between two or more branches.
Node is indicated by dot sign. When a short circuit has two nodes it actually becomes one
node. If we redraw the first circuit as it has two common points shown in black color filled.
After redrawing the circuit becomes as below circuit. It shows three nodes a, b, c.
A loop is any closed path in a circuit.
Loop counts starting at a node passing through a set of nodes and returning to the starting
node without passing through any node more than once.
A loop is said to be independent if it contains at least one branch which is not a part of any
other independent loop. From independent path or independent loop we get independent set
of the equations. We can consider above circuit to define set of loop. For 4Ω resistor consider
with independent 20V voltage source there path abca is a loop. If we think second loop for 6Ω
with independent 4A current source then we get another loop. Such way many set of loop can
be made.
A network with b branches, n nodes and l independent loops will satisfy the fundamental
theorem of network topology,
b=l+n–1
Two or more elements are in series if they exclusively share a single node and consequently
carry the same current.
Two or more elements are in parallel if they are connected to the same two nodes and
consequently have the same voltage across them.
Question: Now tell how many branches and nodes are in below circuit?
Answer: the circuit has five branches as it contains five elements. It has three nodes. Because
short path is counted one node.
Classification of Electrical Network
Electric circuit has many elements like resistor, capacitor, inductor, battery etc. Circuit
analysis is the process by which voltage or current is measured across the element. In a
complete circuit there are two types of elements found active elements and passive elements.
The active elements generate energy. Batteries, generators, operational amplifiers etc are
active elements. The passive elements cannot generate energy, they drop energy. Resistor,
capacitor, inductor etc are passive elements because they takes energy from circuit.
Unilateral/Bilateral Elements
An element whose operational behaviour is dependent on the direction of flow of current
through is known as unilateral elements. Elements like semiconductor diode, which allow the
current to pass through them only in one direction.
An element whose behaviour is same irrespective of the direction of flow of current through it
is known as bilateral element. Passive elements that allow the current to pass through them in
both directions are known as bilateral elements.
Lumped and Distributed Networks
Networks consisting of elements which can be physically separated are known as lumped
networks. Most of the networks we deal with, are lumped in nature and consists of R, L,C and
sources. Networks,
like
transmission
lines,
having
inseparable
elements
are
known
as distributed networks.
Linear and Non-Linear Elements
A linear element is one which has linear output/input relation and always follows superposition
and homogeneity principles. Ohm’s can be applied to such networks. The element that which
does not follow these is known as a nonlinear element. Ohm’s law cannot be applied to such
networks.
Electrical Energy Sources
In a complete circuit voltage or current source are most active elements which deliver power
in the circuit. Two type of source i) independent and ii) dependent source.
An ideal independent source is an active element that provides a specified voltage or current
that is completely independent of other circuit elements.
An ideal voltage source is that element which supply voltage between two terminals to
maintain current through the circuit. Generators, batteries are the ideal voltage sources in
circuits. In figure two dc voltage sources is shown. Figure 1 (a) shows the symbol of time
varying voltage source and figure 1(b) shows continuous dc voltage source.
An ideal independent current source is also an active element which supply a specified current
to a circuit. Figure 2 shows the independent current source symbol where arrow sign indicates
the direction of flowing current i.
An ideal dependent source is an active element in which the source quantity is controlled by
another voltage or current.
Figure 3 shows the symbol of dependent voltage and current source it is diamond shaped.
Dependent source of voltage or current is controlled by other element in the circuit. There are
four types of possible dependent are
i) A current controlled voltage source (CCVS),
ii) A voltage controlled voltage source (VCVS),
iii) A current controlled current source (CCCS),
iv) A voltage controlled current source (VCCS).
In figure 4 a circuit diagram on the right hand side a current controlled voltage source is
shown. Here the voltage is 5i depends on current i through element C. The value of dependent
voltage source is in 5i Volt not in 5i Ampere. Because it is a voltage source. Voltage source has
polarities (+ -) symbols. But current source contains arrow indicating the direction of current.
An ideal dependent or independent voltage source produces any current requires to ensure
that the terminal voltage is as stated. On the other hand an ideal current source produces the
necessary voltage to ensure the stated current flow. In this way an ideal source could in theory
supply an infinite amount of energy. One thing keep it mind that sources not only supply power
to a circuit, they can absorb power from a circuit too.