Dc Circuits

UNIT I

ELECTRICAL CIRCUITS

DC CIRCUITS

The interconnection of various electric elements in a particular manner comprises as an electric circuit in order to perform a desired function. A circuit may be called as direct current (dc) circuit or alternating current (ac) circuit based on the type of components and sources used. If the circuit consists of only elements such as resistor, desired voltage and current sources, then the circuit is called a DC circuit. If the circuit is made up of AC elements like inductor, capacitor and alternating voltage and current sources then the circuit is called as AC circuit.

Circuit laws provide a basis for analyzing the circuits. Ohms law gives the basic relationship between the voltage and current. Kirchoff's laws (KVL and KCL) are useful in deriving the voltage and current equations of a circuit. Mesh and Nodal methods are the systematic approaches of applying Kirchoff's laws to simplify the process of both DC and AC circuit analysis. Further power, power factor and energy are the other complex quantities often used in AC circuit analysis.

Basic Concepts

Charge: The electric charge is the most basic quantity in electrical engineering and arises from the atomic particles of which matter is made. The unit is coulomb. yd novig ei nolaista ni bosqizeib

Potential Difference: The potential difference also known as voltage is the work done to move a unit positive charge from one point to another. The unit is volt.

Current: The electric current is the rate of charge flow in a circuit. The unit is ampere.

Energy: The energy is the capacity to do work. Thus in electrical quantities this may be expressed as:

Power: The electric power is the rate of change of energy The unit is watt.

Electric Circuit: The closed path in which the electrons flow from a voltage or current sources is called an electric circuit.

Circuit Elements: An electrical circuit is an interconnection of electrical circuit elements. These circuit elements can be categorized into two types, namely active elements and passive elements.

* A voltage or current sources of energy (active elements).

* Resistors inductors and capacitors (passive elements).

Passive Elements: The passive elements does not produce any electricity. They may either consume energy or store energy.

Resistors: Resistors are circuit elements that opposes the flow of current.

A pure resistor turns electrical energy into heat.

Current in the Figure 1.1 is entering the + side of the resistor. Resistor doesn't care bas which leg is connected to positive or negative. The + means where the positive or red probe of the voltmeter is to be placed in order to get a positive reading. This is called 'positive' sign convention.

If the current entering the + side of the resistor means that the resistor is removing energy from the circuit.

Relation between resistivity and conductivity:

Resistivity and conductivity are reciprocals.

Energy Stored Elements

Capacitors and Inductors, can store energy to be released back into the circuit under certain conditions.

Inductors:

An inductor is a coil of wire that stores energy in the form form of a magnetic field.

The basic equation governing the behaviour of an inductor is Faraday's law of electromagnetism.

When there are N turns in a coil. emf will be induced in each turn. So that the voltage across the coil would be N times larger. So neglecting the -ve sign.

The flux produced in the magnetic circuit, is proportional to the current flowing in the coil, so that the role of change of flux in terms of a rate of change of current,

The basic electrical circuit equation as:

The stored energy of the inductor w(t)==L.i².

Capacitor:

Capacitors are passive circuit elements that can be used to store energy in the form of an electric field.

The charge stored is directly proportional to the applied voltage,

q=C.V

Since q = Sidt the basic equation for the capacitor may be re-written in the circuit terms as:

Since the current through a capacitor is proportional to the rate of change of voltage, a step voltage change is not possible through a capacitor as this would corresponds to an infinite current.

The energy stored in the capacitor is given by:

Active Circuit Elements

An active circuit element is a component in a circuit which is capable of producing or generating energy. They are divided into two types:

1) Voltage Source

2) Current Source.

Sources can be divided into two types:

1) Independent Source

2) Dependent Source.

Independent Source

For an independent voltage or current source the terminal voltage or current would depend only on the loading and the internal source quantity but not an any other circuit variable.

(i) Independent Voltage Source:

From Figure 1.4(a) an ideal voltage source keeps the voltage across it unchanged independent of load.

From Figure 1.4(b) the practical voltage source have a drop in voltage across their internal impedances. The voltage drop is generally small compared to the internal emf.

Independent Current Source:

From Fig.1.5(a) and ideal current source keeps the circuit produced unchanged independent of load.

From Fig.1.5(b) practical current source have a drop in current across their internal admittances.

The current drop is generally small compared to the internal source current.

Dependent Source

A dependent voltage or current source would have its terminal voltage or current depend on another circuit quantity such as voltage or current. There are four possibilities of dependent source.

(1) Voltage Dependent (controlled) Voltage Source (VDVS).

(2) Current Dependent (controlled) Voltage Source (CDVS)

(3) Voltage Dependent (controlled) Current Source (VDCS).

(4) Current Dependent (controlled) Current Source (CDCS).

Linear and Non-Linear Circuits

(i) Linear Circuit:

An element is said to be linear if its voltage-current characteristics is at all times straight line through the origin.

A linear element or network is one which satisfies the principle of superposition is the principle of homogeneity and additivity.

(ii) Non-Linear Circuit:

A non-linear system is that whose parameters change with voltage or current. It does not obey the law of homogeneity and additive properties.