My Life in CIRCUITS: 2015

Tuesday, March 17, 2015

Three Phase Circuit

The Y Connections

- each phase is connected between a line and the neutral.

Phase Voltage = Line to neutral voltage(Va, etc.).

Phase Currents = Line currents(Ia, etc.).

Neutrals Connect the 3 phases.

The Delta Connections

- each phase is connected in two lines.

Phase Voltage = Line voltages(Vab, etc.).

Phase Currents = Currents from line to line(Iab, etc.).

Neutral is not present.

Definition of the following:

Phase - it is simply the branch of the circuit.

Line - wires that connect the source to the load.

Neutral - the 4th wire in the three phase system. It's where the phases of a Y connection come together.

Line Currents - the current flowing in each of the lines(Ia, Ib, Ic).

Line Voltage - the voltage between any two of the lines(Vab, Vbc, Vac).

Phase Currents & Voltages - the voltages and currents across and through a single branch (phase) of the circuit. It depends on whether the connection is Wye or Delta!

Y connected source

Delta connected source

Y connected load

Delta connected load

Reminders:

All 3 variables have the same amplitude
All 3 variables have the same frequency
All 3 variables are 120^o in phase
All 3 sources are represented by a set of balanced 3-phase variables
All loads are 3-phase with equal impedance's
Line impedance are equal in all 3 phases

Balanced 3-phase circuit:

Sunday, March 15, 2015

Power Factor

- the cosine of the phase difference between voltage and current.

- it is also the cosine of the angle of the load.

Consider this is a circuit:

Find the Power Factor:

First, analyze the circuit.
You can see to the circuit that when you convert the given load into phasor, you can get the angle.
The formula is pf = cos(angle of Z)
The answer must in between Zero to One.
If your answer is greater than 1, it means your answer is wrong.
If it is positive, its LAGGING(inductive).
If it's negative, its LEADING(capacitive).
In the circuit, the complex part is positive, it means LAGGING.
FINISH!!

Apparent Power

Apparent POWER(in VA)

- is the product of the RMS values of voltage and current.

RMS(Root Mean Square)

- arises from the need measure the effectiveness of a voltage or current source

in delivering power to a resistive load.

The incandescent light bulb is a commonly-used resistive load.

Consider this is a circuit.

Find the apparent power of the circuit:

For getting the apparent power.
The formula is S = Vrms Irms
In the formula, the Irms is also unknown.
Therefore, to solve the Apparent Power(S) get first the Irms.
To get the Irms, use Ohm's Law. Don't forget that! :))
Formula for Ohm's Law:

I = Vrms/Z , instead of R.

Then, you can now solve the Apparent Power(S)
FINISH

Tuesday, February 24, 2015

KIRCHOFF'S LAW

FIRST LAW

Kirchoff's Current Law

-the sum of current entering the node

is equal to the current leaving the node

NODE????

- when two or more branches

is connected to each other

BRANCH????

-has a single element

with each terminals

SECOND LAW

Kirchoff's Voltage Law

-states that the sum of voltages in a loop

is always equal zero

LOOP????

- is any continuous path available

for current flow from a given point in a circuit and

back to that same point in the circuit from the

opposite direction that it left from without

crossing or retracing

it`s own path.

LEARNINGS:

For getting the current I3 in the circuit

using KCL process, you must add the current

that enters the node and subtract the current that

leaving the node, then equal to zero.

OHM'S LAW

- states that the current through a conductor between two points is directly proportional to the potential difference across the two points.

Types of Element:

PASSIVE

- is an electrical component that does not generate power,

but instead dissipates, stores, and/or releases it.

ACTIVE

- generate energy.

Short circuit

- that allows a current to travel along

an unintended path.

Open circuit

- it lacks a complete path between the

terminals of its power source

LEARNING'S:

You can see to this picture that when the voltage is bigger,

the current will also become bigger.

And when the resistance of the resistor is big,

the current will decrease.

But, when the resistance of the resistor is small,

the current that enters the resistor will be bigger.

Therefore, as we change the value of the voltage

and the resistance of the resistor,

the current also change.

VOLTAGE

- is the FORCE

CURRENT

- is the MOTION

RESISTOR

- is the FRICTION

Introduction of Electric Circuit

This includes the definition of various electrical quantities and their relationships.

CHARGE(q)
CURRENT(i)
POWER(p)

CHARGE(q)

- is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.

- The symbol Q is often used to denote a charge.

- The unit of electric charge is the coulomb(c).

Two types of electric charges
positive(+) charge
negative(-) charge

POSITIVE CHARGE(+)

- having a deficiency of electrons.
- having higher electric potential.

NEGATIVE CHARGE(-)

- a charge that has more electrons than protons and has a lower electrical potential.

Formula for getting charge

q = ʃ idt

CURRENT(i)

- is a flow of electric charge.

- In electric circuits this charge is often carried by moving electrons in a wire.

- unit for measuring an electric current is the ampere.

Formula for getting current

i = dq/dt

POWER(p)

- the rate at which electrical energy is transferred by a circuit.

Capacitor and Inductor

Capacitor

-(originally known as a condenser)

is a passive two-terminal electrical component used to store

energ electro-statically in an electric field.

Consider this is a circuit:

For Computing the Capacitor equivalet

IN PARALLEL

IN SERIES

Inductor

-also called a coil or reactor, is a passive two-terminal electrical component which resists changes in electric current passing through it. It consists of a conductor such as a wire, usually wound into a coil. When a current flows through it, energy is stored temporarily in a magnetic field in the coil.

THEVENIN THEOREM AND NORTON EQUIVALENT

Thevinen

-Any linear electrical network with voltage and current sources and only resistances can be replaced at terminals A-B by an equivalent voltage source V_th in series connection with an equivalent resistance R_th.

Norton

- Consist of a single current source and a single parallel resistor.

For the Thevinen equivalent voltage

For the Norton equivalent current

MESH ANALYSIS

- it is a technique which relies on KVL.

Consider this is a circuit, with two meshes 1 and 2

Next, assume current flow clockwise(CW) for easier.
Define two mesh current I1 and I2.
Then, assign voltage polarities to all resistor.
Use KVL in loop 1 and 2 to get the equation.
But, in R3 there are two current flow I1 and I2
So, we write it in this manner -R3(I1-I2) for loop one and for loop two - R3(I2-I1)
Loop 1 equation: 3 - R1I1 - R3(I1-I2) = 0
For Loop 2 equation: 10 - R3(I2-I1) - R2I2 = 0
We can now substitute the value of the resistors, and expand it.