gel104 dc circuits

7/27/2019 GEL104 DC Circuits

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GEL104:

PRINCIPLES OF ELECTRICAL ENGINEERING

Dr. Nitin K. GoelDepartment of Electrical Engineering

IIT Ropar

Room No. - 228

Email: [email protected]

Web: http://nkgoel.tech.officelive.com


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DC CIRCUITS


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Electrical circuits can get quite complex. But at the simplest

level, you always have the source of electricity (a battery,

etc.), a load (a light bulb, motor, etc.), and two wires to carry

electricity between the battery and the load. Electrons move

from the source, through the load and back to the source.

Electrical Circuits


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DC Circuits

An Ideal DC circuit (Direct Current Circuit) is an electrical circuit that

consists of any combination of constant voltage sources, constant

current sources, and resistors. In this case, the circuit voltages and

currents are constant,

i.e., independent of time.

More technically, a DC circuit has no memory. That is, a particular circuit

voltage or current does not depend on the past value of any circuit

voltage or current. This implies that the system of equations that represent a DC circuit do

not involve integrals or derivatives (no time dependency).


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DC Circuits

If a capacitor and/or inductor is added to a DC circuit, the resulting

circuit is not, strictly speaking, a DC circuit. However, most such

circuits have a DC solution. This solution gives the circuit voltages

and currents when the circuit is in DC steady state.

More technically, such a circuit is represented by a system of

differential equations. The solution to these equations usually

contain a time varying or transient part as well as constant or

steady state part. It is this steady state part that is the DC solution.

There are some circuits that do not have a DC solution. Two simpleexamples are a constant current source connected to a capacitor

and a constant voltage source connected to an inductor.


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DC Circuits

In electronics, it is common to refer to a circuit that is

powered by a DC voltage source such as a battery or

the output of a DC power supply as a DC circuit even

though what is meant is that the circuit is DC powered.


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CIRCUIT PRINCIPLES

Interconnection of several Circuit Elements Electrical Circuit

Circuits of Considerable Complexities Networks

Network Theorems: Circuit Principles that are capable of general

applications in electrical networks.

Linear Networks Combination of components represented by Ideal

R, L and C and Ideal energy sources V and I

Branch: Part of a circuit with two terminals for connection.

Node: Merging point of two or more branches

Loop: A closed path formed by connecting branches


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KCL and KVL

Kirchhoffs Current Law (KCL) and Kirchhoffs Voltage Law (KVL) are

the fundamental laws of circuit analysis.

KCL is the basis of nodal analysis in which the unknowns are the

voltages at each of the nodesof the circuit.

KVL is the basis of mesh analysis in which the unknowns are the

currents flowing in each of the meshesof the circuit.


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KIRCHOFF CURRENT LAW

This fundamental law results from the conservation of charge. It

applies to ajunction or node in a circuit -- a point in the circuit

where charge has several possible paths to travel.

IA is the only current flowing intothe node. However, there arethree paths for current to leave the node, and these current are

represented by IB, IC, and ID.

Once charge has entered into the node, it has no place to go

except to leave (this is known as conservation of charge). Thetotal charge flowing intoa node must be the same as the the

total charge flowing out ofthe node. So,IB + IC + ID = IA

Bringing everything to the left side of the above equation, we get(IB + IC + ID) - IA = 0

Then, the sum of all the currents is zero.


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KIRCHOFF CURRENT LAW

The algebraic sum of all currents

entering a node is zero, or

The sum of currents entering node is

equal to sum of currents leaving node.

=

=

n

j

ji

1

0

Note the convention we have chosen in previous slide:

Current flowing intothe node are taken to be negative,

Currents flowing outofthe node are positive. It should not really matter which you choose to be the positive or

negative current, as long as you stay consistent.


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KIRCHOFF VOLTAGE LAW

- It states that the algebraic sum of the voltages

around a closed loop must be zero at any instant.

0

1

=

=

n

jjv

Here the total voltage around loop 1 should sum to

zero, as does the total voltage in loop2.

Furthermore, the outer loop of the circuit (the pathABCD) should also sum to zero.

We can adopt the convention that potential gains(i.e. going from lower to higher

potential, such as with an EMF source) is taken to be positive. Potential losses(such as across a resistor) will then be negative.

However, as long as you are consistent in doing your problems, you should be able

to choose whichever convention you like.


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NETWORK THEOREMS

AND

ANALYSIS


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LINEAR CIRCUIT

Voltage across a resistor varies proportionally with its current.

A linear circuit consists of linear elements. The passive elements, the dependentsources and the independent sources used in a linear circuit are linear.

Linearity is between the flux linkage and the current

Linearity is between the charge stored and the capacitor voltage

Linearity of Elements


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SUPERPOSITION THEOREM

The superposition theorem is a method of solving circuits, often used in Linear

circuits with more than one EMF source. It uses Kirchhoff's Voltage Law.

Limitations: Applied only to linear effects such as the current response

The strategy used in the Superposition Theorem is to eliminate all but

one source of power within a network at a time, using series/parallel

analysis to determine voltage drops (and/or currents) within the

modified network for each power source separately.

Once voltage drops and/or currents have been determined for each

power source working separately, the values are all superimposed on

top of each other (added algebraically) to find the actual voltagedrops/currents with all sources active.


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There are two guiding properties Linearity (Proportionality)- Effect (y) is directly proportional to

the cause (x) y=f(x)

Additivity


This theorem states that the linear responses in a circuit with

multiple sources can be obtained as the algebraic sum of

responses, due to each of the independent sources acting alone.

If f is linear f(x+dx)=f(x)+f(dx) y+dy


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Example of Superposition Theorem


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+



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An equivalent circuit refers to the simplest form of a

circuit that retains all of the electrical characteristics of

the original (and more complex) circuit.

In its most common form, an equivalent circuit is made

up of linear, passive elements.

Two circuits are equivalent if they present the same V-I

characteristics.

EQUIVALENT CIRCUIT


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PARALLEL DC CIRCUIT

=


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SERIES-PARALLEL DC CIRCUIT

=


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Thevenins Theorem

Any black box containing only voltage sources, currentsources, and other resistors can be converted to aThvenin equivalent circuit, comprising exactly onevoltage source and one resistor.


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In circuit theory, Thvenin's theorem for linear electrical networksstates that any combination of voltage sources, current sources,

and resistors with two terminals is electrically equivalent to a singlevoltage source Vand a single series resistor R.

For single frequency AC systems the theorem can also be applied

to general impedances, not just resistors.

The theorem was first discovered by German scientist Hermann

von Helmholtz in 1853[1], but was then rediscovered in 1883 by

French telegraph engineer Lon Charles Thvenin (18571926).

Thvenin's Theorem


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Calculate the output current, IAB, when the output terminals are

short circuited (load resistance is 0). RTh equals VTh divided by thisIAB.

Calculating the Thvenin equivalent

To calculate the equivalent circuit, the resistance and voltage are

needed, so two equations are required. These two equations areusually obtained by using the following steps:

Calculate the output voltage, VAB, when in open circuit condition

(no load resistormeaning infinite resistance). This is VTh.

The equivalent circuit is a voltage source with voltage VTh inseries with a resistance RTh.


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Example

Step 0: The original circuit Step 1: Calculating the

equivalent output voltage

Step 2: Calculating theequivalent resistance

Step 3: The equivalent circuit


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In the example, calculating the equivalent voltage

(notice that R1 is not taken into consideration, as above calculations are done in anopen circuit condition between A and B, therefore no current flows through this partwhich means there is no current through R

1and therefore no voltage drop along

this part)

Calculating equivalent resistance:

Example (Contd.)

gel104 dc circuits

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