DC Circuits Notes PDF

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Summary

This set of notes contains fundamental knowledge of Basic Electrical Engineering and fundamental elements required.
Topics include
1. Introduction
2. Voltage and Current sources (Independent)
3. Ideal Voltage Source
4. Ideal Current Source
5. Passive Components

Description

DC Circuits Notes Introduction 1. Electric circuit has many elements like resistor, capacitor, inductor, battery etc. 2. Circuit analysis is the process by which voltage or current is measured across the element. 3. In a complete circuit, there are two types of elements found active elements and passive elements. 4. The active elements generate energy: Batteries, generators, operational amplifiers etc are active elements. 5. The passive elements cannot generate energy; they drop energy. 6. Resistor, capacitor, inductor, etc. are passive elements because they takes energy from circuit. 7. In a complete circuit voltage or current source are most active elements, which deliver power in the circuit. 8. An independent source can deliver or absorb energy continuously (without any limit) such element are called active element. 9. Two type of source a. Independent, and b. Dependent source. 10. An ideal independent source is an active element that provides a specified voltage or current that is completely independent of other circuit elements. 11. An ideal voltage source is that element which supply voltage between two terminals to maintain current through the circuit.

Voltage and Current sources (Independent) An ideal independent voltage/current source is also an active element, which supply a specified voltage/current to a circuit. On the other hand, an ideal dependent source is an active element in which the source quantity is controlled by another voltage or current. Dependent source of voltage or current is controlled by other element in the circuit. There are four types of possible dependent are I. II. III. IV.

A current controlled voltage source (CCVS), A voltage controlled voltage source (VCVS), A current controlled current source (CCCS), A voltage controlled current source (VCCS).

Ideal Voltage Source A voltage source is a two-terminal device whose voltage at any instant of time is constant and is independent of the current drawn from it. Such a voltage source is called an Ideal Voltage Source and have zero internal resistance. Practically an ideal voltage source cannot be obtained. Sources having some amount of internal resistances are known as Practical Voltage Source, due to this internal resistance; voltage drop takes place, and it causes the terminal voltage to reduce.

Ideal Current Source An Ideal current source is a two-terminal circuit element, which supplies the same current to any load resistance connected across its terminals. It is important to keep in mind that the current supplied by the current source is independent of the voltage of source terminals. It has infinite resistance.

Passive Components Components that cannot provide any power gain to the circuit are called passive devices. These devices are incapable of controlling the current (energy) flow in the circuit and need the help of active devices to operate. Some examples for passive devices are resistors, inductors and capacitors. Although passive components cannot amplify a signal with a gain more than one, they can multiply a signal by a value less than one. They also can oscillate, phase shift and filter signals. Some passive components also have the capability to store energy (drawn from an active element) and release later. Example: capacitors and inductors.

Resistance When a voltage is applied across a metallic conductor, (say copper), the electric field created accelerates the conduction (free) electrons. These electrons collide with metal ions of the crystal lattice (of the metal) and lose part of their energy as heat. Repeated accelerations and collisions cause two components of electron motion, the drift (average velocity) and the random motion. The drift of electrons that constitutes the electric current in the conductor (the conventional current flows in the opposite direction) which is associated with energy loss in the form of heat. Therefore, the resistance is a dissipative element, which converts electric energy into heat, when the current flows through it in any direction. This process of energy conversion is irreversible.

Ohm’s Law This is the most fundamental law in Electrical Engineering. It states that the potential difference between the two ends of a conductor is directly proportional to the current flowing through it, provided its temperature and other physical parameters remain unchanged. That is, V ∝ I or V = RI

(2.1)

The constant of proportionality R is called the resistance of the conductor. Its unit is ohm (Ω). The unit ohm defined as the resistance, which permits a flow of one ampere of current when a potential difference of one volt is applied to the resistance. There is another way of stating Ohm's law, I∝V or I = GV

(2.2)

The constant of proportionality G is called the conductance of the conductor. Comparison of Eq. 2.2 with Eq. 2.1 shows that the conductance is the reciprocal of the resistance, G = 1/R

(2.3)

The SI unit of conductance is Siemens (S).

Short Circuit and Open Circuit These two are special resistances. A short circuit (R = 0) permits current to flow (I ≠ 0) without any resulting voltage (V = 0). An open circuit (R = ∞) permits voltage (v ≠ 0) with no current (I = 0). Since power going into a resistance is p = VI, no power is required for the short circuit or the open circuit.

Switches An ideal switch is also a special resistance. It can be changed from a short circuit to an open circuit to turn an electrical device ON and OFF. Ideal switches receive no electrical energy from the circuit.

Series Combination of Resistance Two or more resistances are said to be connected in series, if same (not merely equal) current flows through them. Let us assume the same current I flows through the three resistances. The applied voltage must be equal to the sum of the three individual voltages, V₁, V₂, and V3 That is,

V = V₁ + V₂ + V₁ = IR₁ + IR₂+ IR3 = I(R₁ + R₂+ R₂)

(2.4)

We can write, V = IR,

(2.5)

From Eq. 2.4 and Eq. 2.5, it can be seen that R₁ =R₁+R₂+ R3 Thus, the equivalent resistance of a number of resistances connected in series is equal to the sum of individual resistances. In general, for n resistances in series, we can write 

𝑅  𝑅₁  𝑅₂  𝑅 . . . 𝑅𝑛   𝑅𝑗 

Parallel Combination of Resistance Two or more resistances are said to be connected in parallel, if same (not merely equal) voltage exists across them. Since the total current I entering the combination divides into I1, I2 and I3, we have I=I1+1₂+13= V/R1 + V/R2 + V/R3 = V (1/R1 + 1/R2 + 1/R3)

(2.6)

We can write, I = V/Rp Comparing Eq. 2.6 and 2.7, we get 1/Rp = 1/R1 + 1/R2 + 1/R3

(2.7)

Thus, the reciprocal of equivalent resistance of a number of resistances connected in parallel is equal to the sum of the reciprocals of the individual resistances. In general, for n resistances in parallel, we can write  



















⋯





 ∑





(2.8)...