CAPACITOR AND INDUCTOR

CAPACITOR AND INDUCTOR

CAPACITOR
-A capacitor is a two-terminal, electrical component. Along with resistors and inductors, they are one of the most fundamental passive components we use. You would have to look very hard to find a circuit which didn’t have a capacitor in it.

A capacitor, we are familiar with this thing because we use to it into our power supply. We use capacitor to stored energy in our power supply.

INDUCTOR
-An inductor is a passive electronic component that storesenergy in the form of a magnetic field. In its simplest form, an inductor consistsof a wire loop or coil. The inductance is directly proportional to the number ofturns in the coil.

The standard unit of inductance is the henry.

In a capacitor, the formula is expressed as “the current in a circuit is in proportion to the time rate of change of the voltage across it.

written as:

i=c(dv/dt)

In series and parallel capacitors, they are combined in the same way as conductances.

An inductor formula states that the voltage across it is directly equitable to the rate of change of the current through the circuit.

The formula is written like this:

v=L(di/dt)

In solving inductors in series and parallel, it is the same as combining the resistors in the circuit, which is in series or parallel.

FIRST ORDER CIRCUITS: SOURCE FREE RC AND RL CIRCUIT

FIRST ORDER CIRCUITS: SOURCE FREE RC AND RL CIRCUIT

FIRST ORDER CIRCUIT
-A circuit that can be simplified to a Thevenin's or Norton's equivalent connected to either a single equivalent inductor or capacitor.

THE SOURCE-FREE RC CIRCUIT
-an electric circuit composed of resistors and capacitorsdriven by a voltage or current source. A first order RC circuit is composed of one resistor and one capacitor and is the simplest type of RC circuit.

IN SOLVING THE RC CIRCUIT

The time required for the voltage to fall to is called the RC time constant and is given by

SOURCE FREE RL CIRCUIT
-is an electric circuit composed of resistors and inductorsdriven by a voltage or current source. A first order RL circuit is composed of one resistor and one inductor and is the simplest type of RL circuit.

IN SOLVING THE RL CIRCUIT

SAMPLE RL CIRCUIT

MAXIMUM POWER TRANSFER

MAXIMUM POWER TRANSFER THEOREM

maximum power transfer theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must equal the resistance of the source as viewed from its output terminals. 

(RTH=RL)

PROVE THAT RL=RTH

Computing the Power Transfer is equal to V2/4(RL) 

THEVENIN'S AND NORTON'S THEOREM

THEVENIN'S  AND NORTON'S THEOREM

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. It is especially useful in analyzing power system and another circuits where one particular resistor in the circuit called the load resistor is subject to change and re-calculation of the circuit is necessary with each trial value of load resistance to determine voltage and current across it.

It is also states that the linear two terminal circuit can be replaced by an equivalent circuit consisting of a voltage source VTH in a series resistor RTH where Vth is the open circuit voltage at terminals and Rth is the input or total resistance at the terminals when the independent source are turn off.



There are two cases you need to consider in thevenin's:

Case 1: If the network has no dependent source therefore you need to turn off all independent source. Rth can be computed via parallel or series connection seen from the given.

Case 2: If the network has dependent source turn off all dependent source. Apply V0 at A-b and Also Io at A-b.


Thevenins Equivalent Circuit:

NORTON'S THEOREM

-Any collection of batteries and resistances with two terminals is electrically equivalent to an ideal current source i in parallel with a single resistor r. The value of r is the same as that in the Thevenin equivalent and the current i can be found by dividing the open circuit voltage by r.

Norton's Circuit

Norton's Equivalent Circuit:

SAMPLE PROBLEM:

LINEARITY PROPERTY, SUPERPOSITION AND SOURCE TRANSFORMATION

*LINEAR PROPERTY

-linear network consist of linear elements, linear dependent sources and linear independent sources.

It is state that the output of linear circuit is directly proportional to its input.

LINEAR SYSTEM HAVE TWO IMPORTANT AND USEFUL PROPERTIES:
-Superposition
-Homogeneity





*SUPERPOSITION
- Superposition states that the voltage across an element in linear circuit is the algebraic sum of the  voltages across that element due to each independent source acting alone.



WAYS OR TECHNIQUES IN SOLVING THIS CIRCUIT:

-Turn off, killed, inactive source:
-independent voltage source: 0 V (short circuit)
-independent current source: 0 A (open circuit)
-Dependent sources are left intact.

After you apply those techniques above, proceed to the steps in solving superposition.

STEPS TO APPLY THE PRINCIPLE:
1.Turn off all independent sources except one source. Find the output voltage or current due to that active source using mesh analysis or nodal analysis.

2.Repeat step 1 with other independent sources.
3.Find the total contribution by adding directly all of the contributions of independent sources.

In killing the independent sources, first you need to turn off all the sources(current and voltage) short the voltage source and open the current source and make their voltages and currents equal to zero.



SAMPLE OF A SUPERPOSITION CIRCUIT:

SAMPLE PROBLEM:

Find the voltage Vx using superposition

*SOURCE TRANSFORMATION
-Source transformation talks about simplifying a circuit especially with complicated or mixed sources. By transforming the voltage sources into current sources and current sources into voltage sources using ohms law V=IR.

Sample Problem :

(this sample problem is unfinish but we only post this sample in order to explain properly the transformation)