Basic Engineering

Alternating Current (AC):   Most students of electricity begin their study with what is known as  direct current (DC), which is electricity flowing in a constant direction, and/or possessing a voltage with constant polarity. DC is the kind of electricity made by a battery (with definite positive and negative terminals), or the kind of charge generated by rubbing certain types of materials against each other. As useful and as easy to understand as DC is, it is not the only “kind” of electricity in use. Certain sources of electricity (most notably, rotary electro-mechanical generators) naturally produce voltages alternating in polarity, reversing positive and negative over time. Either as a voltage switching polarity or as a current switching direction back and forth, this “kind” of electricity is known as Alternating Current (AC): Figure below distribution systems that are far more efficient than DC, and so we find AC used predominately across the world in high po...

Norton's Theorem:  Norton's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single current source and parallel resistance connected to a load. Just as with Thevenin's Theorem, the qualification of "linear" is identical to that found in the Superposition Theorem: all underlying equations must be linear (no exponents or roots). Contrasting our original example circuit against the Norton equivalent: it looks something like this: . . . after Norton conversion . . . Remember that a  current source  is a component whose job is to provide a constant amount of current, outputting as much or as little voltage necessary to maintain that constant current. As with Thevenin's Theorem, everything in the original circuit except the load resistance has been reduced to an equivalent circuit that is simpler to analyze. Also similar to Thevenin's Theorem are the steps used in Norto...

loop and nodal methods of analysis : We have seen that using Kirchhoff’s laws and Ohm’s law we can analyze any circuit to determine the operating conditions (the currents and voltages).  The challenge of formal circuit analysis is to derive the smallest set of simultaneous equations that completely define the operating characteristics of a circuit. In this lecture we will develop two very powerful methods for analyzing any circuit: The node method and the mesh method. These methods are based on the systematic application of Kirchhoff’s laws. We will explain the steps required to obtain the solution by considering the circuit example shown on Figure 1. Node Method:  A voltage is always defined as the potential difference between two points. When we talk about the voltage at a certain point of a circuit we imply that the measurement is performed between that point and some other point in the circuit. In most cases that other point is referred to as ground.  The...

Bilateral element:   Conduction of current in both directions in an element (example: Resistance; Inductance; Capacitance) with same magnitude is termed as bilateral element. Unilateral Element:   Conduction of current in one direction is termed as unilateral (example: Diode, Transistor) element.

Maximum Power Transfer Theorem : The Maximum Power Transfer Theorem is not so much a means of analysis as it is an aid to system design. Simply stated, the maximum amount of power will be dissipated by a load resistance when that load resistance is equal to the Thevenin/Norton resistance of the network supplying the power. If the load resistance is lower or higher than the Thevenin/Norton resistance of the source network, its dissipated power will be less than maximum. This is essentially what is aimed for in stereo system design, where speaker "impedance" is matched to amplifier "impedance" for maximum sound power output. Impedance, the overall opposition to AC and DC current, is very similar to resistance, and must be equal between source and load for the greatest amount of power to be transferred to the load. A load impedance that is too high will result in low power output. A load impedance that is too low will not only result in low power output, bu...

Introduction to network theorems: Anyone who's studied geometry should be familiar with the concept of a  theorem : a relatively simple rule used to solve a problem, derived from a more intensive analysis using fundamental rules of mathematics. At least hypothetically, any problem in math can be solved just by using the simple rules of arithmetic (in fact, this is how modern digital computers carry out the most complex mathematical calculations: by repeating many cycles of additions and subtractions!), but human beings aren't as consistent or as fast as a digital computer. We need "shortcut" methods in order to avoid procedural errors. In electric network analysis, the fundamental rules are Ohm's Law and Kirchhoff's Laws. While these humble laws may be applied to analyze just about any circuit configuration (even if we have to resort to complex algebra to handle multiple unknowns), there are some "shortcut" methods of analysis to make the...

Mesh current method: The  Mesh Current Method  is quite similar to the Branch Current method in that it uses simultaneous equations, Kirchhoff's Voltage Law, and Ohm's Law to determine unknown currents in a network. It differs from the Branch Current method in that it does  not  use Kirchhoff's Current Law, and it is usually able to solve a circuit with less unknown variables and less simultaneous equations, which is especially nice if you're forced to solve without a calculator. Let's see how this method works on the same example problem: The first step in the Mesh Current method is to identify "loops" within the circuit encompassing all components. In our example circuit, the loop formed by B 1 , R 1 , and R 2  will be the first while the loop formed by B 2 , R 2 , and R 3  will be the second. The strangest part of the Mesh Current method is envisioning circulating currents in each of the loops. In fact, this method gets its name from th...

Source Transformation :  In an electric circuit, it is often convenient to have a voltage source rather than a current source (e.g. in mesh analysis) or vice versa. This is made possible using source transformations. It should be noted that only practical voltage and current sources can be transformed. In other words, a Th´evenin’s equivalent circuit is transformed into a Norton’s one or vice versa. The parameters used in the source transformation are given as follows. Any load resistance, RL will have the same voltage across, and current through it when connected across the terminals of either source. Example:  In given figure, use repeated source transformation to determine the current through the5Ωresistance. Noting that the voltage source and the 10 Ω resistor are in series, transform the combination into a current source in parallel with the 10 Ω resistor. The magnitude of the current source is calculated as follows        ...

DC Sources:  In general, there are two main types of DC sources  Independent (Voltage and Current) Sources  Dependent (Voltage and Current) Sources An independent source produces its own voltage and current through some chemical reaction and does not depend on any other voltage or current variable in the circuit. The output of a dependent source, on the other hand, is subject to a certain parameter (voltage or current) change in a circuit element. Herein, the discussion shall be confined to independent sources only. DC Voltage Source:  This can be further subcategorised into ideal and non-ideal sources. The Ideal Voltage Source An ideal voltage source, shown in Figure (a), has a terminal voltage which is independent of the variations in load. In other words, for an ideal voltage source, the supply current alters with changes in load but the terminal voltage, VL always remains constant. This characteristic is depicted in given figure(b). Non-Ideal or P...

Branch current method: The first and most straightforward network analysis technique is called the  Branch Current Method . In this method, we assume directions of currents in a network, then write equations describing their relationships to each other through Kirchhoff's and Ohm's Laws. Once we have one equation for every unknown current, we can solve the simultaneous equations and determine all currents, and therefore all voltage drops in the network. Let's use this circuit to illustrate the method: The first step is to choose a node (junction of wires) in the circuit to use as a point of reference for our unknown currents. I'll choose the node joining the right of R 1 , the top of R 2 , and the left of R 3 . At this node, guess which directions the three wires' currents take, labeling the three currents as I 1 , I 2 , and I 3 , respectively. Bear in mind that these directions of current are speculative at this point. Fortunately, if it turns out ...

Thevenin's Theorem: Thevenin's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load. The qualification of "linear" is identical to that found in the Superposition Theorem, where all the underlying equations must be linear (no exponents or roots). If we're dealing with passive components (such as resistors, and later, inductors and capacitors), this is true. However, there are some components (especially certain gas-discharge and semiconductor components) which are nonlinear: that is, their opposition to current  changes  with voltage and/or current. As such, we would call circuits containing these types of components,  nonlinear circuits . Thevenin's Theorem is especially useful in analyzing power systems and other circuits where one particular resistor in the circuit (called the "load" resistor) is subject t...

Polarity of voltage drops:    We can trace the direction that electrons will flow in the same circuit by starting at the negative (-) terminal and following through to the positive ( ) terminal of the battery, the only source of voltage in the circuit. From this we can see that the electrons are moving counter-clockwise, from point 6 to 5 to 4 to 3 to 2 to 1 and back to 6 again. As the current encounters the 5 Ω resistance, voltage is dropped across the resistor's ends. The polarity of this voltage drop is negative (-) at point 4 with respect to positive ( ) at point 3. We can mark the polarity of the resistor's voltage drop with these negative and positive symbols, in accordance with the direction of current (whichever end of the resistor the current is  entering  is negative with respect to the end of the resistor it is  exiting : We could make our table of voltages a little more complete by marking the polarity of the voltage for each pair of poin...