Elementary Concepts and DC Circuits
Elementary Concepts and DC Circuits
Elementary Concepts
Covers resistance, EMF, current, potential difference, and Ohm’s law.
Provides an overview of an elementary power system, illustrating the stages of generation, transmission, and distribution of electrical energy.
Elementary Power System Overview
Generation: The initial stage where electrical energy is produced (e.g., power plants).
Transmission: The process of carrying electrical energy over long distances, typically at high voltages (e.g., transmission lines, substations).
Distribution: The delivery of electrical energy to end-users at lower voltages (e.g., distribution centers, local networks).
Resistance
A resistor is a two-terminal electrical component that restricts current flow in a circuit.
This restriction leads to a voltage drop across the resistor.
Types and Applications of Resistors
Applications include high-frequency instruments, DC power supplies, filter circuits, oscillators, voltage regulators, medical instruments, digital multimeters, transmitters, power control, amplifiers, telecommunications, wave generators, modulators, demodulators, and feedback amplifiers.
Inductance
Inductance is the property of a wire (often coiled) that opposes changes in the current flowing through it.
Changing current induces an electromotive force (EMF) in the coil, according to Faraday’s law of electromagnetic induction.
The magnitude of the EMF is proportional to the rate of change of current.
The proportionality constant is the inductance (measured in Henrys, H).
Named after Joseph Henry who discovered electromagnetic induction around 1831.
Capacitance
Capacitance is the ability to store energy in the form of an electrical charge.
Capacitors consist of two conducting plates separated by an insulator (dielectric).
Dielectric materials include ceramic, film, glass, or air which enhances the charging capacity.
Ohm's Law
The relationship between voltage (V), current (I), and resistance (R) is defined as:
V = I \times R
R = V/I
Resistance in Series
When resistors are connected in series, the current through each resistor is the same.
The total voltage across the series combination is the sum of the individual voltages across each resistor.
Resistance in Parallel
The total resistance of resistors in parallel is calculated using the formula:
\frac{1}{R{\text{Total}}} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3}
For three resistors, the formula simplifies to:
R{\text{total}} = \frac{R1 \cdot R2 \cdot R3}{R1 + R2 + R_3}
Power Supply System
Generation System: Includes power stations generating electricity at 11 kV, 11.5 kV, or 12 kV.
Transmission System: Transports power over long distances at high voltages (220 kV).
Primary Transmission: Uses voltages like 220 kV.
Secondary Transmission: Uses voltages like 132 kV or 66 kV.
Distribution System: Delivers power to local areas.
Primary Distribution: Typically at 11 kV.
Secondary Distribution: Steps down voltage to 400 V and 230 V for consumers.
Load Center: Where the electricity is consumed.
Power Plants in Supply System
Thermal Power Plant
Hydroelectric Power Plant
Nuclear Power Plant
Renewable Power Plant
Components of Electrical Engineering
Generation Plants: Thermal, Hydroelectric, Renewable, Nuclear
Generators: AC/DC, 3-phase AC (50Hz, 11 KV-22 KV)
Prime Movers
Transmission: Transformers (11KV to 220 KV/ 500 KV), Transmission Lines, Substations (HV)
Distribution Main Components: Transformers (220 KV to 132 KV, 132 KV to 11KV, 11KV to 400V), Transmission Lines, Substations (LV)
Loads:
Electrical: Motors, household applications, lighting, etc.
Mechanical: Pulleys, fans, flooring machines, blowers, etc.
Voltage Levels in Power Systems
Transmission Networks: Operate at 765kV / 400kV / 220kV AC or 500kV DC (EHV AC or HVDC).
AC Sub-Transmission Networks: Operate at 132kV / 110kV / 66kV / 33kV AC.
AC Distribution Networks: Operate at 11kV primary and 400V secondary AC.
Household: Operates at 230V, 50 Hz, single phase.
Generation Networks: Generate at 11kV to 12kV AC (EHV AC).
Classification of Electrical Networks
Linear Network: Parameters (resistance, inductance, capacitance) are constant regardless of time, voltage, or temperature.
Ohm’s law applies.
Superposition can be used.
Non-linear Network: Parameters change with time, temperature, or voltage.
Ohm’s law may not apply.
Superposition may not hold.
Bilateral Network: Characteristics are the same regardless of current direction.
Resistive networks are examples.
Unilateral Network: Behavior depends on the direction of current.
Diode circuits are examples.
Active Network: Contains an energy source (voltage or current).
Passive Network: Contains no energy source.
Lumped Network: Network elements are physically separable.
Distributed Network: Network elements are not physically separable (e.g., transmission lines).
Circuit Concepts
Series Circuits
Parallel Circuits
Current and Voltage Division
Series vs. Parallel Comparison
Simplification of Networks
Using series-parallel combinations
Numerical examples
Current Divider Rule (CDR)
Used to divide current among parallel resistors.
i1 = \frac{R2}{R1 + R2} \times I_T
i2 = \frac{R1}{R1 + R2} \times I_T
Voltage Divider Rule
Used to determine voltage distribution in a series circuit.
V{\text{out}} = \frac{Rb}{Ra + Rb} \times V_{\text{in}}
where:
V_{\text{out}} is the output voltage
Ra and Rb are resistors in series
V_{\text{in}} is the input voltage
Kirchhoff’s Laws
Kirchhoff’s Current Law (KCL)
Kirchhoff’s Voltage Law (KVL)
Kirchhoff's Current Law (KCL)
The algebraic sum of currents entering and leaving a node is zero.
Kcl states that total current flowing towards a junction point is equal to total current flowing away from that junction.
\sum I = 0
Kirchhoff's Voltage Law (KVL)
The algebraic sum of the potential differences (voltages) around any closed loop is zero.
KVL states that , “In any network algebriac sum of voltage drop across circuit elements is equal to algebraic sum of emfs in that path“.
\sum V = 0
KVL Sign Conventions
Potential Drop: Movement from higher to lower potential (negative sign).
Potential Rise: Movement from lower to higher potential (positive sign).
In a simple circuit: -I R1 - I R2 + V = 0 which leads to V = I(R1 + R2), and I = \frac{V}{R1 + R2}
Applications of Kirchhoff’s Laws
KCL: Analyze total current in a complex circuit.
KVL: Analyze total voltage in a complex circuit.
Together, they form Kirchhoff’s Circuit Law.
Steps to Apply KCL
Locate nodes.
Assign current variables and directions.
Write KCL equation: ∑Iin=∑Iout
Solve for unknown currents (use Ohm’s Law if needed).
Validate: Ensure ∑Iin=∑Iout∑Iin=∑Iout
Steps to Apply KVL
Identify all closed loops in the circuit.
Assign a current direction to each loop.
Mark voltage polarities based on current direction.
Write the KVL equation for each loop: ∑V=0∑V=0
Sum voltage drops and rises
Loop Analysis Using KCL and KVL
Draw a closed loop and indicate the direction of current flow.
Define sign conventions for voltage drops and rises.
Apply KCL at nodes (e.g., I1 + I2 = I_3).
Apply KVL around the loops.
Example Equations from Loop Analysis
Loop 1: 10 = R1 I1 + R3 I3 = 10 I1 + 40 I3 (simplified to 1 = I1 + 4 I3)
Loop 2: 20 = R2 I2 + R3 I3 = 20 I2 + 40 I3 (simplified to 1 = I2 + 2 I3)
Combined: 10 - 20 = 10 I1 - 20 I2 (simplified to 1 = -I1 + 2 I2)
Solving for Currents
Using KCL, I1 + I2 = I_3, equations are reduced and solved to find the currents in each loop/branch.
Advantages and Limitations of Kirchhoff’s Laws
Advantages:
Ease of calculating unknown voltages and currents.
Simplification of complex closed-loop circuits.
Limitations:
Assumes no fluctuating magnetic fields in the closed loop.
Varying magnetic fields can induce electric fields and electromotive force, breaking Kirchhoff’s rule.
Star-Delta/Delta-Star Transformation
Technique to simplify networks.
Delta to Star Conversion:
RA = \frac{R1 R2}{R1 + R2 + R3}
RB = \frac{R2 R3}{R1 + R2 + R3}
RC = \frac{R1 R3}{R1 + R2 + R3}
Star to Delta Conversion:
R1 = \frac{RA RB + RB RC + RA RC}{RC}
R2 = \frac{RA RB + RB RC + RA RC}{RA}
R3 = \frac{RA RB + RB RC + RA RC}{RB}
If RA = RB = RC = R{\text{delta}}, then R{\text{star}} = \frac{R{\text{delta}}}{3}
If R1 = R2 = R3 = R{\text{star}}, then R{\text{delta}} = 3 R{\text{star}}
Need for Star-Delta Conversion
Simplifies complex resistor networks for easier analysis.
Superposition Theorem
In a linear, bilateral network with multiple energy sources, the current through a branch is the algebraic sum of the currents produced by each source acting independently.
When considering each source, other voltage sources are short-circuited and current sources are open-circuited.
Steps for Superposition Theorem
Consider one voltage source at a time, replacing others with short circuits.
Calculate the current through the desired element.
Repeat for each voltage source.
Algebraically sum the individual currents to find the total current.
Superposition Theorem: Equations Considering Two Voltage Sources
Considering source V1:
(R1 + R2) I1' - R2 I2' = V1
-R2 I1' + (R2 + R3) I_2' = 0
Solve for I1' and I2', then I' = I1' - I2'
Considering source V2:
(R1 + R2) I1'' - R2 I_2'' = 0
-R2 I1'' + (R2 + R3) I2'' = -V2
Solve for I1'' and I2'', then I'' = I1'' - I2''
Total current: I = I' + I''
Numerical Practice
KVL using loop equation (6-8 marks)
Equivalent resistance, Series-parallel circuit simplification (6 marks)
Star - Delta circuit simplifications (6-8 marks)
Superposition theorem (6-8 marks)
Questions for Unit No.1
Numerical
KVL using loop equation (6-8 marks)
Superposition theorem (6-8 marks)
Star - Delta circuit simplifications (6-8 marks)
Series-parallel circuit simplification (6-8 marks)
Derivations
Delta- Star conversion and vice versa (6-8 marks)
Theory Questions
Electrical Power System block diagram ( Including in detail explanation of voltage levels, etc.) (6-8 marks)
Network Classification (1 mark each)
KCL/ KVL with detail explanation (4 marks)
Superposition theorem with explanation (6 - 8 marks)