Advanced Electrical Theory


Capacitors are energy storage devices which have the ability to store an electrical charge across its plates. The simplest construction of a capacitor is by using two parallel conducting metal plates separated through a distance by an insulating material.

The larger the area of the plates or the smaller their separation the more charge the capacitor can store. Capacitance is measured in Farads, which is a very large unit so micro-Farad (μF), nano-Farad (nF) and pico-Farad (pF) are generally used.


In its most basic form, an Inductor is nothing more than a coil of wire wound around a central core. Forming a wire coil into an inductor results in a much stronger magnetic field than one that would be produced by a simple coil of wire.

Unlike a Capacitor which oppose a change of voltage across their plates, an inductor opposes the rate of change of current flowing through it due to the build up of self-induced energy within its magnetic field. Inductance which is given the symbol L with units of Henry, (H). It is also common to see inductance expressed in smaller units like millihenry.


A device that transfers electric energy from one alternating-current circuit to one or more other circuits, either increasing (stepping up) or reducing (stepping down) the voltage. Primary winding refers to the higher voltage and the Secondary winding refers to the lower voltage.


A diode is a specialized electronic component that acts as a one-way switch. It conducts electric current in only one direction and restricts current from the opposite direction. A diode is reverse biased when it acts as an insulator and is forward biased when it allows current to flow.

A diode has two terminals, the anode and the cathode. The voltage applied to the anode is positive with respect to the cathode. Also, the voltage in the diode is higher than the threshold voltage, so it acts as a short circuit and allows current to flow.

If the cathode is made positive with respect to the anode, the diode is reverse-biased. It will then act as an open circuit that results in no flow of current. Diodes are usually used to construct different types of rectifier circuits such as half-wave, full-wave, center-tapped and full bridge rectifiers.


A Transistor is a three terminal semiconductor device that regulates current or voltage flow and acts as a switch or gate for signals. In its basic form, a transistor is simply a combination of two diodes connected at various junction points.

Biasing is controlling the operation of the circuit by providing power supply. The function of both junctions is controlled by providing bias to the circuit through some dc supply. Transisors are commonly used for extremely fast switching and pulse width modulation found in AC inverters.


  • Emitter: As this emits electrons, it is called as an Emitter.
  • Base: Its main function is to pass the majority carriers from the emitter to the collector.
  • Collector: its function of collecting the carriers.

Inductive and Reactive Loads

In an alternating current system, current occurs in sine waves according to the frequency of the power source. In a circuit unaffected by inductance or reactance, voltage and current would rise and fall together during each cycle. This condition, known as unity.

In practice, circuits present inductive or reactive characteristics that cause voltage and current to peak at separate times in an ac cycle.

  • In inductive circuits, voltage leads current.
  • In capacitive circuits, voltage lags current.

Greater amounts of time between current and voltage peaks indicate a greater amount of inductive or capacitive load, and either condition increases the work needed to deliver the required amount of real power to loads.

voltage with a leading and lagging current, plotted against time.
Voltage with a leading and lagging current, plotted against time.

Basic Power Factor

The extent to which the voltage and current peak at separate times is quantified by the power factor. For purely resistive loads, power factor equals 1. Increasing variance from this value indicates decreasing amounts of real power available for work.

The classic beer analogy is often used to help you to better understand power factor:

The drinkable portion of a beer is represented by Real Power (expressed in kW). Real Power may also be called Actual Power, Active Power or Working Power. This is what actually powers electrical equipment and performs useful work (in this case, quenching your thirst).

Along with the brew comes a little bit of foam, and that foam just isn’t going to do anything useful, so consider this undrinkable portion of the beer to be Reactive Power, represented by KVAR. This is the power that magnetic equipment like transformers, motors and relays need to produce their magnetizing flux. Think of the foam as a reaction from pouring the beer.

The combination of drinkable beer (kW) and foam (kVAR) inside of your mug represents the Apparent Power, or KVA.

Power Factor is simply the ratio of Real Power (kW) to Apparent Power (kVA) and is represented by the following formula: PF = KW / KVA.

Using our beer analogy you could write the formula like this: PF = Beer / Drinkable Beer + Foam.

Leading and Lagging Power Factor

Power factor is described as leading if the current leads voltage, or lagging when the current lags voltage. A lagging power factor signifies that the load is inductive, as the load will “consume” reactive power. A leading power factor signifies that the load is capacitive, and the load will “produce” reactive power.

Examples of lagging and leading power factors.
Examples of lagging and leading power factors.

Power Factor is most affected by reactive loads. Reactive power charges occur when the power factor of a building falls below a certain level, typically defined by the electricity supplier (average is around 0.95 and below).

  • Perfect PF = 1.00 (unlikely to achieve).
  • Good = 1.0 – 0.95
  • Poor = 0.95-0.85
  • Bad = 0.85 and below.