ELECTRICAL CIRCUITS-1 (THEORY)

1. Circuit parameters

(66721  )   ELECTRICAL CIRCUITS-I                                                                                                              

1.1. Define direct current (DC)

Direct current (DC) is the unidirectional flow of an electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or even through a vacuum as in electron or ion beams. The electric current flows in a constant direction, distinguishing it from alternating current (AC). A term formerly used for this type of current was galvanic current.^[1]

1.2. Define circuit parameters.

What are the basic electrical parameters?

1.3. List the circuit parameters.

What is a Circuit or Electric Circuit?

Circuit or electrical circuit is a close loop path giving a return path for the current. Or a close conducting path in which current can flow is called circuit.

1.4. Define circuit parameters with units.

Resistance is a value which measure how much the component “resist” the passage of electrical current, the value is measured in ohms (Ω). One way to calculate resistance:

$R=\rho \frac{L}{A}$R=ρAL​

• $\rho$ρ is the resistivity, a material’s property.

Another form to calculate the resistance is applying Ohm’s law.

$R=\frac{V}{I}$R=IV​ is the voltage and $I$ is the current.

Ideal circuit elements. Introduction to the most common circuit elements: resistor, capacitor, and inductor.

An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, current sources, resistances, inductances, capacitances). An electrical circuit is a network consisting of a closed loop, giving a return path for the current. 

Capacitance

Capacitance is the capacity to store energy in a capacitor, is measured in farads (F), these are capacitors.

Capacitance is calculated in this form:

$C=\frac{Q}{V}$C=VQ​

• $Q$Q is the charge and $V$V is the voltage.

The capacitance in a capacitor with parallel plates.

$C=\epsilon \frac{A}{d}$C=ϵdA​

• $\epsilon$ϵ is the electric permissiveness;
• $A$A is the plate area;
• $d$d is the distance between plates.

Inductance

While the capacitor stores energy in an electrical field, the inductor stores energy in a magnetic field. Inductance is the inductor’s capacity to resist variation of electric current and is measured in henries (H). The inductor is nothing more than a rolled wire in spirals which can have a nucleus inside to increase the magnetic field and the inductance. Here are various types of inductors. Sometimes inductors are called solenoids.

The formula to calculate inductance:

$L=\frac{\mu N^{2}A}{l}$L=lμN2A​

• $\mu$μ is the magnetic permeability;
• $N$N is the number of spires or turns in the inductor;
• $A$A is the section area;
• $l$l is the length.

The inductor’s association in series and in parallel is equal to the resistors and the total inductance is calculated in the same way.

Impedance and Reactance

In alternated current, the value of resistance in the passive components (resistor, capacitor and inductor) is called impedance, which is formed by reactances. In the resistor the impedance is equal the resistance value in the CC. In capacitors and inductors, the reactance is an imaginary number and are called respectively capacitive reactance and inductive reactance.

Capacitive reactance.

$X_{c}=\frac{1}{\omega C}$Xc​=ωC1​

• $C$C is the capacitance and $\omega$ω is the circuit’s frequency in radians/s.

Inductive reactance.

$X_{l}=\omega L$Xl​=ωL

This graphic shows the impedance as Z, reactances as $X_{c}$Xc​ and $X_{l}$Xl​ in the imaginary axis and the resistance in the real numbers axis.

A number of electrical laws apply to all electrical networks. These include:

• Kirchhoff's current law: The sum of all currents entering a node is equal to the sum of all currents leaving the node.
• Kirchhoff's voltage law: The directed sum of the electrical potential differences around a loop must be zero.
• Ohm's law: The voltage across a resistor is equal to the product of the resistance and the current flowing through it.
• Norton's theorem: Any network of voltage or current sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor.
• Thévenin's theorem: Any network of voltage or current sources and resistors is electrically equivalent to a single voltage source in series with a single resistor.
• Superposition theorem: In a linear network with several independent sources, the response in a particular branch when all the sources are acting simultaneously is equal to the linear sum of individual responses calculated by taking one independent source at a time.

Other more complex laws may be needed if the network contains nonlinear or reactive components. Non-linear self-regenerative heterodyning systems can be approximated. Applying these laws results in a set of simultaneous equations that can be solved either algebraically or numerically.

2. Electric Network

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2.1. Define electric networks.

An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, current sources, resistances, inductances, capacitances).

What is an Electrical Network?

Combination of different electric elements or components which are connected in any way is called electric network

Complex Networks

A Circuit which contains on many electrical elements such as resistors, capacitors, inductors, current sources and Voltage source (both AC and DC) is called Complex network. These kinds of networks can’t be solved easily by simple ohm’s Law or Kirchhoff’s laws. I.e. we solve these circuits by specific technique i.e. Norton’s Theorem, Thevenin’s Theorem, Superposition theorem etc.  

2.2. Explain the different types of electric networks.

There are many types of electrical circuits such as:

• Series Circuit
• Series Circuit
• Series-Parallel Circuit
• Star-Delta Circuit
• Resistive Circuit
• Inductive Circuit
• Capacitive Circuit
• Resistive, Inductive (RL Circuit)
• Resistive, Capacitive (RC Circuit)
• Capacitive, Inductive (LC Circuits)
• Resistive, Inductive, Capacitive (RLC Circuit)
• Linear Circuit
• Non Linear Circuit
• Unilateral Circuits
• Bi-lateral Circuits
• Active Circuit
• Passive Circuit
• Open Circuit
• Short Circuit

2.3. Explain the different types of electric networks.

2.4. Define active and passive network.

ACTIVE CIRCUIT

A circuit which contains on one or more E.MF (Electro motive force) sources is called Active Circuit

PASSIVE CIRCUIT

A circuit, in which no one EMF source exist is called Passive Circuit

• The Main Difference between Active and passive Components (Very Easy Explanation with Examples)

2.5. Define current source and voltage source.

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2.6. Explain the current and voltage source in electric network.

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2.7. Give example of current source & voltage source.

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3. Circuit Theorems

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3.1. State & explain Kirchhoff’s current Law (KCL) and Kirchhoff’s voltage Law (KVL).

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3.2. State & explain Thevenin’s theorem.

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3.3. State & explain Superposition theorem.

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3.4. State & explain Norton’s theorem.

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3.5. State & explain Maxwell’s theorem.

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3.6. State & explain Maximum power transfer theorem.

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3.7. Solve problems related to all Theorems.

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4. Star-Delta Conversion

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4.1. State star-delta conversion.

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4.2. Explain star-delta conversion.

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4.3. Convert star to delta connection and vice versa.

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4.4. Solve problems related to star-delta conversion.

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5. AC circuit and AC fundamentals.

5.1. Define AC circuit (AC).

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5.2. Explain the importance of AC systems.

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5.3. Describe the advantages and disadvantages of AC circuit.

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5.4. Principle of the generation of AC voltage.

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5.5. Derive the equation: e = EmaxSinωt

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5.6. Define cycle, frequency & time period with units.

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5.7. Show the relation: f = PN 120

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5.8. List the commercial frequency of different countries

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5.9. Explain phase & phase difference with diagram.

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5.10. Solve related problems.

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6. Alternating quantities and rms values.

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6.1. Define instantaneous values, average and maximum values of alternating quantities.

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6.2. Generalize the rms values.

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6.3. 6 Define form factor and peak factor.

6.3 Define form factor and peak factor.

6.4. Define ohmic resistance & effective resistanc

6.4 Define ohmic resistance & effective resistance.

6.5. Compare ohmic & effective resistan

6.5 Compare ohmic & effective resistance.

6.6. Solve problems on instantaneous, average and rms values.

6.6 Solve problems on instantaneous, average and rms values.

7. Vectors and vector quantities.

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7.1. Define vector quantities.

7.1 Define vector quantities.

7.2. Explain vector representation of alternating voltage and current

7.2 Explain vector representation of alternating voltage and current.

7.3. Explain vector in Polar form.

7.3 Explain vector in Polar form.

7.4. Explain vector in Rectangular form.

7.4 Explain vector in Rectangular form.

7.5. Formulate the relation between vectors expressed in rectangular and polar co-ordinate

7.5 Formulate the relation between vectors expressed in rectangular and polar co-ordinate.

7.6. Solve problems relating to vector sum & difference, multiplication and division

7.6 Solve problems relating to vector sum & difference, multiplication and division.

8. AC circuit (containing pure resistance, inductance and capacitance)

AC circuit (containing pure resistance, inductance and capacitance).

8.1. Sketch a circuit containing pure Resistance.

8.1 Sketch a circuit containing pure Resistance.

8.2. Explain the vector & phasor diagram of a pure resistive circuit.

8.2 Explain the vector & phasor diagram of a pure resistive circuit.

8.3. Deduce the current and voltage relation in pure resistive circuit.

8.3 Deduce the current and voltage relation in pure resistive circuit.

8.4. Sketch a circuit containing pure Inductance.

8.4 Sketch a circuit containing pure Inductance.

8.5. Explain the vector & phasor diagram of pure Inductive circuit.

8.5 Explain the vector & phasor diagram of pure Inductive circuit.

8.6. Evaluate the relation among inductive reactance, current and voltage in pure Inductive circuit.

8.6 Evaluate the relation among inductive reactance, current and voltage in pure Inductive circuit.

8.7. Sketch a circuit containing pure Capacitance.

8.7 Sketch a circuit containing pure Capacitance.

8.8. Explain the vector & phasor diagram of pure capacitive circuit.

8.8 

8.9. Formulate capacitive reactance

8.9 Formulate capacitive reactance.

8.10. Simplify current and voltage relation in pure capacitive circuit.

8.10 Simplify current and voltage relation in pure capacitive circuit.

9. AC series circuit (containing resistance, inductance and capacitance).

9. AC series circuit (containing resistance, inductance and capacitance).

9.1. Draw circuit containing resistance and inductance (RL) in series.

9.1 

9.2. Explain vector & phasor diagram in RL series circuit.

9.2 Explain vector & phasor diagram in RL series circuit.

9.3. Formulate impedance, current and voltage drop in RL series circuit.

9.3 Formulate impedance, current and voltage drop in RL series circuit.

9.4. Draw impedance triangle in RL series circuit.

9.4 Draw impedance triangle in RL series circuit.

9.5. Draw circuit containing resistance and capacitance (RC) in series.

9.5 Draw circuit containing resistance and capacitance (RC) in series.

9.6. Explain vector & phasor diagram in RC series circuit.

9.6 Explain vector & phasor diagram in RC series circuit.

9.7. Formulate impedance, current and voltage drop in RC series circuit.

9.7 Formulate impedance, current and voltage drop in RC series circuit.

9.8. Draw impedance triangle of RC series circuit.

9.8 Draw impedance triangle of RC series circuit.

9.9. Solve problems on RL & RC series circuits.

9.9 Solve problems on RL & RC series circuits.

9.10. Sketch a circuit containing resistance, inductance and capacitance (RLC) in series.

9.10 Sketch a circuit containing resistance, inductance and capacitance (RLC) in series.

9.11. Explain vector & phasor diagram of RLC series circuit.

9.11 Explain vector & phasor diagram of RLC series circuit.

9.12. Draw impedance triangle of RLC series circuit.

9.12 Draw impedance triangle of RLC series circuit.

9.13. Calculate inductive reactance, capacitive reactance, total impedance, current & voltage drop in RLC series circuit.

9.13 Calculate inductive reactance, capacitive reactance, total impedance, current & voltage drop in RLC

series circuit.

9.14. Solve problems on RLC series circuit.

9.14 Solve problems on RLC series circuit.

10. Power & power factor in AC circuit.

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10.1. Define power, power factor, active & reactive power.

10.1 Define power, power factor, active & reactive power.

10.2. Calculate power and power factor of pure resistive circuit.

10.2 Calculate power and power factor of pure resistive circuit.

10.3. Calculate power and power factor of pure Inductive circuit.

10.3 Calculate power and power factor of pure Inductive circuit.

10.4. Calculate power and power factor of pure capacitive circuit.

10.4 Calculate power and power factor of pure capacitive circuit.

10.5. Calculate power, power factor, active & reactive power of RL, RC & RLC series circuit.

10.5 Calculate power, power factor, active & reactive power of RL, RC & RLC series circuit.

10.6. Explain the power diagram of R, L, C, RL, RC & RLC series circuit.

10.6 Explain the power diagram of R, L, C, RL, RC & RLC series circuit.

10.7. Solve problems on power & power factor of different series circui

10.7 Solve problems on power & power factor of different series circui