Series and Parallel Connections

What are "series" and "parallel" circuits?

Circuits consisting of just one battery and one load resistance are very simple to analyze, but they are not often found in practical applications. Usually, we find circuits where more than two components are connected together.

There are two basic ways in which to connect more than two circuit components: series and parallel. First, an example of a series circuit: 

Here, we have three resistors (labeled R₁, R₂, and R₃), connected in a long chain from one terminal of the battery to the other. (It should be noted that the subscript labeling -- those little numbers to the lower-right of the letter "R" -- are unrelated to the resistor values in ohms. They serve only to identify one resistor from another.) The defining characteristic of a series circuit is that there is only one path for electrons to flow. In this circuit the electrons flow in a counter-clockwise direction, from point 4 to point 3 to point 2 to point 1 and back around to 4.

The equivalent resistance of any number of resistors connected in series the sum of the individual resistances. 

For N resistors in series,

To determine the voltage across each resistor,

Now, let's look at the other type of circuit, a parallel configuration: 

Again, we have three resistors, but this time they form more than one continuous path for electrons to flow. There's one path from 8 to 7 to 2 to 1 and back to 8 again. There's another from 8 to 7 to 6 to 3 to 2 to 1 and back to 8 again. And then there's a third path from 8 to 7 to 6 to 5 to 4 to 3 to 2 to 1 and back to 8 again. Each individual path (through R₁, R₂, and R₃) is called a branch.

The defining characteristic of a parallel circuit is that all components are connected between the same set of electrically common points. Looking at the schematic diagram, we see that points 1, 2, 3, and 4 are all electrically common. So are points 8, 7, 6, and 5. Note that all resistors as well as the battery are connected between these two sets of points.

As for a parallel circuit, the equivalent resistance of two parallel resistors is equal to the product of their resistances divided by their sum,

Or in general,

To get the current in a parallel circuit, we may use,

 And, of course, the complexity doesn't stop at simple series and parallel either! We can have circuits that are a combination of series and parallel, too:

In this circuit, we have two loops for electrons to flow through: one from 6 to 5 to 2 to 1 and back to 6 again, and another from 6 to 5 to 4 to 3 to 2 to 1 and back to 6 again. Notice how both current paths go through R₁ (from point 2 to point 1). In this configuration, we'd say that R₂ and R₃ are in parallel with each other, while R₁ is in series with the parallel combination of R₂ and R₃.

The basic idea of a "series" connection is that components are connected end-to-end in a line to form a single path for electrons to flow: 

The basic idea of a "parallel" connection, on the other hand, is that all components are connected across each other's leads. In a purely parallel circuit, there are never more than two sets of electrically common points, no matter how many components are connected. There are many paths for electrons to flow, but only one voltage across all components: 

Series and parallel resistor configurations have very different electrical properties.

Basic Laws - Part II

I'm back!!! Where was I again? Oh, that was about Ohm's law, wasn't it? So, let's pick up the pace and continue with Kirchhoff, okay? :)

So, we know now about Georg Simon Ohm and his contribution to our daily life. How about Gustav Robert Kirchhoff?

Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws.

Both of Kirchhoff's laws can be understood as corollaries of the Maxwell equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits.

 

Kirchhoff's Voltage Law - KVL - is one of two fundamental laws in electrical engineering, the other being Kirchhoff's Current Law (KCL). 

• KVL is a fundamental law, as fundamental as Conservation of Energy in mechanics, for example, because KVL is really conservation of electrical energy.
• KVL and KCL are the starting point for analysis of any circuit.
• KCL and KVL always hold and are usually the most useful piece of information you will have about a circuit after the circuit itself.
 

Kirchhoff's current law (KCL)

This law is also called Kirchhoff's first law, Kirchhoff's point rule, or Kirchhoff's junction rule (or nodal rule).

The principle of conservation of electric charge implies that:

At any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node, or:

The algebraic sum of currents in a network of conductors meeting at a point is zero.

Recalling that current is a signed (positive or negative) quantity reflecting direction towards or away from a node, this principle can be stated as:

 

n is the total number of branches with currents flowing towards or away from the node.

This formula is valid for complex currents:

The law is based on the conservation of charge whereby the charge (measured in coulombs) is the product of the current (in amperes) and the time (in seconds).

A matrix version of Kirchhoff's current law is the basis of most circuit simulation software, such as SPICE. Kirchhoff's current law combined with Ohm's Law is used in nodal analysis.

Kirchhoff's voltage law (KVL)

This law is also called Kirchhoff's second law, Kirchhoff's loop (or mesh) rule, and Kirchhoff's second rule.

The principle of conservation of energy implies that

The directed sum of the electrical potential differences (voltage) around any closed network is zero, or: 

More simply, the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop, or: 

The algebraic sum of the products of the resistances of the conductors and the currents in them in a closed loop is equal to the total emf available in that loop.

Similarly to KCL, it can be stated as:

Here, n is the total number of voltages measured. The voltages may also be complex:

This law is based on the conservation of energy whereby voltage is defined as the energy per unit charge. The total amount of energy gained per unit charge must equal the amount of energy lost per unit charge, as energy and charge are both conserved.

The videos below will help you understand more about Kirchhoff's law.

That's it guys!!! Tune in again for more lessons!!

GOD Bless!!! :D