July 11, 2009

Electrical Circuits

Laws of Resistance

1. The resistance of a conductor varies directly as its length.

2. The resistance of a conductor varies inversely to its cross section area.

3. The resistance of a conductor depends on the material.

4. The resistance of a conductor depends on its temperature.

The above factors can be summed up mathematically as :

laws of resistance

where ρ is constant representing the nature of material and is known as specific resistance.

Effect of Temperature on Resistance

(a) Resistance of pure metals and alloys increases with rise in temperature.

(b) Resistance of electrolytes, insulators and semiconductors decreases with rise in temperature.

If Ro = Conductor resistance at 0˚C

Rt = Conductor resistance at t˚C

t = rise in temperature

and αo = Temperature coefficient of resistance at 0˚C,

Then Rt = Ro (1 + αot)

The temperature coefficient at 0˚C is defined at the change in resistance per ohm for a rise in temperature of 1˚C from 0˚C.

Grouping of Cells

A single cell has an e.m.f. of about 1.5 volts. If either more voltage is needed or more current is required, then cells are connected either in series or in parallel respectively. This arrangement of connection is named as grouping of cells.

Cells in Series

When cell are connected in series, e.m.f. of the battery is equal to the sum of the e.m.f. of cells.

Internal resistance of battery =sum of internal resistance of cells.

e.m.f. of battery E =ne

where e is e.m.f. of the cell and n refers to the number of cells in series.

Cells in Parallel

The cells when arranged in parallel have the same e.m.f., but internal resistance of the unit is reduced.

If n cells are connected in parallel, each of e.m.f. E,


e.m.f. of the battery = e.m.f. of one cell = E

cells in parallel

where r is the resistance of one cell

Cells in Series and in Parallel

n = number of cells in each row

m = number of parallel rows.

N = total number of cells = mn.

Let e.m.f of one cell =e

E.M.F. of battery =ne volts

Internal resistance of each row =nr ohms

cells in series and in parallel

Cell Efficiency

The efficiency of a Cell is considered in two ways:

(1) Ampere-hour (A.h) efficiency.

(2) Watt-hour (W.h.) efficiency.

cell efficiency

D.C. Motors

D.C. motors are classified according to the method of excitation. They may be of the shunt, series or compound types.

Series Motor

The speed of a series motor is given by the relation:

series motor

series motor

Shunt motor

shunt motor

where Ra is the armature resistance. Since is practically constant at all loads, speed is there almost constant.

Types of Armature Winding

The two main types of winding are:

  1. Lap Winding. It is also known as parallel winding or multiple winding. In this type of winding, the numbers of parallel paths (A) are equal to the number of poles (P).

  2. Wave Winding. In this case the armature conductors are divided into two parallel irrespective of the number of poles.


The rotor of induction motor rotates at somewhat lesser speed than the synchronous speed and actual speed is known as slip.


where Nr is rotor or actual while N is synchronous speed.


AC through Resistance and Inductance

In the resistance part of the circuit the current is in phase with the voltage, while in the inductive part it is 90˚ out of phase. Hence, to determine the current, the effect of resistance and reactance has to be combined which is named as impedance:

ac through resistance and inductance

where is the phase angle between the voltage and current and cos is called the power factor.

Circuits Containing Resistance, Inductance and Capacitance

circuit containing resistance, inductance and capacitance


Transformer is a device for transferring energy from one alternating current circuit to another without any change in frequency. It changes voltage from high to low and low to high with a corresponding increase or decrease in current. If the voltage is increased, the transfer is said to be stepped up. If it is decreased, then it is referred as step down.


Three Phase Transformer

Whenever the supply is three phase and it is desired to transform current at another voltage, then either a single three phase transformer or three separate single phase transformers can be used. However, in practice a single three phase transformer is used. The three phase winding of a transformer can be connected either in star or in delta.

Current and voltage in star

The e.m.f. between any line and the neutral gives the phase voltage while the e.m.f. between two outer terminals is known as line voltage.

Current in each line is the same as phase current

i.e. Line current IL=Phase current IP

three phase transformer, current and voltage in star

Line Voltage and Current in Delta

line voltage and current in delta


Ohm's Law

ohm's law


I = current, amp

V = potential difference, volts

R = resistance, ohms




ρ = resistivity or specific resistance, ohm-m

L = length of wire, m

A = cross-sectional area of wire, m2

Conductance (G)



γ = conductivity or specific conductance, mhos/m

Electric Power

electric power


P = electric power, watts

Electric Energy

electric energy

where, E = electric energy, Joules

V = potential difference, Volts

I = Current, Amperes

R = resistance, ohms

t = time, seconds

E = 0.24I2Rt, cal

For Battery

electric energy for battery


electric energy for battery

Kirchhoff’s Law

(i) The algebraic sum of all the currents directed towards a junction point is zero.

(ii) The algebraic sum of all the voltage rise taken in a specified direction around a closed circuit is zero.

Series Circuits:

series circuits

Parallel Circuits:

parallel circuits

Coulomb’s Law

The force acting between two charged bodies q1 and q2 in air is proportional to the product of charges and inversely proportional to the square of the distance between them.

Car Anti-Theft Wireless Alarm

Car Anti-Theft Wireless Alarm

This alarm circuit is an anti- theft wireless alarm can be used with any vehicle having 6- to 12-volt DC supply system. The mini VHF FM radio-controlled, FM transmitter is fitted in the vehicle at night when it is parked in the car porch or car park.

Click image for better quality.

The receiver unit of the wireless alarm uses an CXA1019, a single IC-based FM radio module, which is freely available in the market at reasonable rate, is kept inside. Receiver is tuned to the transmitter's frequency. When the transmitter is on and the signals are being received by FM radio receiver, no hissing noise is available at the output of receiver. Thus transis- tor T2 (BC548) does not conduct. This results in the relay driver transistor T3 getting its forward base bias via 10k resistor R5 and the relay gets energised.

When an intruder tries to drive the car and takes it a few metres away from the car porch, the radio link betw- een the car (transmitter) and alarm (receiver) is broken. As a result FM radio module gene-rates hissing noise. Hissing AC signals are coupled to relay switching circ- uit via audio transformer. These AC signals are rectified and filtered by diode D1 and capacitor C8, and the resulting positive DC voltage provides a forward bias to transistor T2. Thus transistor T2 conducts, and it pulls the base of relay driver transistor T3 to ground level. The relay thus gets de-activated and the alarm connected via N/C contacts of relay is switched on.

If, by chance, the intruder finds out about the wireless alarm and disconnects the transmitter from battery, still remote alarm remains activated because in the absence of signal, the receiver continues to produce hissing noise at its output. So the burglar alarm is fool-proof and highly reliable. (Ed: You may have some problem catching the thief, though, if he decides to run away with your vehicle_in spite of the alarm!)

Lessons in DC Circuits

Lessons in Electric circuits Volume I - DC

Master Index
  • Chapter 2: OHM'S LAW
  • Chapter 13: CAPACITORS
  • Chapter 15: INDUCTORS
  • Appendix 1: ABOUT THIS BOOK
  • Appendix 2: CONTRIBUTOR LIST
Download Link :

Electronic Concepts

Electronic Concepts First Edition

Written by Bill

This e-book teaches you all the very basic concepts in electronics in a simple manner

Download Link : http://rapidshare.com/files/254415102/Basics_of_Electronics.rar

A-Z Circuit Symbols

The following table covers almost every circuit symbol you will need. This is the English/American version of each symbol. The European version of some symbols is slightly different and are shown further down the page.


Here are a few notes on the symbols above.

Fuses (10.1a) have single role in a circuit - to detect excess current and protect the device. In most cases the excess current flows when a higher voltage is present but a fuse cannot detect the voltage - it can only detect when a higher current flows. The higher voltage causes the higher current to flow and this triggers the action of "blowing the fuse." Of course, when a component fails, a higher current can flow and this will also "blow the fuse."
Fuses come in all sizes and ratings (current flow) and it is important to know that the size of the wire inside a fuse does not necessarily indicate the current rating.
The wire inside can be made from copper and plated to protect it from oxidizing or it can be a low temperature material that needs to be a larger diameter.
The wire can also be wound in a spiral and formed into a spring. The end of the spring sits in a dob of solder and when the spring heats up, the solder melts and the spring separates from the other end.
This is called a DELAY FUSE.
Other forms of delay fuse consist of a wire joined at the centre by a dob of solder and others are made of low-temperature-melting material.
Some pieces of equipment use expensive fuses and whenever a fuse is damaged, you must decide if the problem is a major or minor fault.
Sometimes a fuse can go open-circuit for no apparent reason. It can "wear-out."
For instance, some equipment takes a very high current when it is turned on and you will see the fuse heat up and stretch and dip in the middle. This causes strain on the fuse and eventually the wire oxidizes to a point where it finally "burns out."
The equipment is not faulty and it is just a matter of replacing the fuse.
Sometimes the fuse completely explodes and the glass is thrown all over the chassis. This indicates a short-circuit in the power supply and most often one or more of the diodes must be replaced.
The fuse can also go off with a "bang" and the inside of the glass is coated with "silver." This also indicates a diode is damaged in the power supply. Generally 2 or 4 diodes are damaged.
If the fuse is damaged beyond recognition, you will not know if it is a delay fuse or a normal fuse.
The current-rating on the end-cap can sometimes help you.
For instance, if a fuse is rated at 4A, you will need to replace it with a 4 amp normal fuse or 3.15 amp slow-blow.
When fuses are rating at 100mA to 250mA, they are very delicate and will not accept the slightest overload.
When replacing this type of fuse, it is necessary to determine if the equipment is drawing a heavy current when turning on or if a fault exists in the power supply. Sometimes the switch can cause the problem if it is not making contact fast enough.
Replace the fuse and watch it as someone else turns on the equipment. If the fuse burns out immediately, a short exists. If the fuse glows red and burns out, the equipment is drawing too much current during turn-on. This may be due to devices you have added to the equipment or operation on a slightly higher voltage. You can try a fuse with a slightly higher rating to see if the fault is fixed.
Never replace a 100mA fuse with a 1 amp fuse. The 1 amp fuse will never "blow" and if the transformer is being overloaded, the transformer will simply "cook."

Lamps (10.1b) Ordinary electric light globes heat a coil of tungsten wire inside a glass bulb that has an inert gas such as argon. The resistance of the filament depends on the temperature it is heated to. It can be ten to twenty times higher than when it is cold.
A neon lamp (10.1c) contains a gas (such as neon) and this gas gives off a glow when a high voltage is applied to two plates. This glow occurs at about 70v to 90v and a resistor must be used in series to prevent the voltage rising higher than required by the lamp. To put this more accurately, the resistance of the neon lamp reduces when it "strikes" and a high current will flow. To limit this current a "current limit" resistor is needed.

VDR (10.1d) The resistance of a VDR depends on the voltage across it. A VDR is also called a VARISTOR. Its resistance is high until a critical value of voltage and the resistance suddenly drops. They are used as voltage protection devices. If they, for example, see a voltage higher than 220V, their resistance decreases and this “soaks” the excess voltage. Their response time is only a few 10's of nanoseconds.

The symbol for a single DC cell is shown in 10.1e.
A Quartz crystal is shown in 10.1f. It is a thin sheet of quarts material between two metal plates and packaged in a metal case. Quartz crystals are commonly used as the reference for an oscillator circuit, such as a clock source in microprocessor designs.
An instrument for measuring current (A) and voltage (V) is shown in 10.1g. This symbol dates from the time when analog instruments with a needle were used. The symbol remains the same, although digital instruments have replaced analog devices.
AC voltage symbol is shown in 10.1h. The shape of the wave is shown in the symbol. It can be sine-wave or saw-tooth or square-wave.
The simplest form of switch device is displayed in 10.1i. Because of the wide range of switches, there are many different types in use. For example, a two pole switch (10.1j) has two operating positions, in one position it connects points 1 and 2, and in the other it connects points 1 and 3.
There are switches with more operating positions. 10.1k is an example of a rotary switch with four positions.

Momentary switches, or push buttons have a built-in spring, which makes the switch conduct only while it is being pressed (your standard doorbell has this kind of switch).
Four diodes in a single case is called a BRIDGE. Two pins are marked with sine waves, used to connect to the AC voltage and two marked with "+" and "-"

RELAY When an electromagnet receives sufficient voltage on points 4 and 5, connection between points 2 and 3 is opened, and at the same time points 3 and 1 are closed. A relay is actually an electromagnetic switch.

Symbols for a receiving and transmitting antenna are shown.
Grounding symbols Grounding and common ground aren't the same thing, but if both exist in a circuit, they are always connected to each other. With electronic devices housed in a metal case, grounding is connected to the metal housing.

Schematic symbols representing logic gates and different digital integrated circuits are shown above. It should be kept in mind that basic logic gates (AND, OR, XOR, Inverter, etc.) aren't manufactured as single standalone components. They are always integrated in groups in an IC, but for the sake of clarity, they are represented as separate blocks. These components require a DC voltage, which may or may not be represented on the schematic. These voltages might be different depending on the internal structure and technology used between different family types. Detailed info on this can be found in the component's datasheet provided by the manufacturer.


Electronics is the study and use of electrical that operate by controlling the flow of electrons or other electrically charged particles in devices such as thermionic valves. and semiconductors. The pure study of such devices is considered as a branch of physics, while the design and construction electronic circuits to solve practical problems is called electronic engineering.

Popular article