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BEEE UNIT-1 DC CIRCUITS - Part 1: Basic Electrical Concepts 1.1 Electric Current Flow of free electrons is called electric current. When electric pressure is applied to a copper strip, free electrons being negatively charged will start moving towards positive terminal around the circuit. This directed flow of electron is called electric current. The convention current flows from positive terminal of source to negative terminal of source (opposite to the flow of electrons). The strength of electric current I is the rate of flow of electrons: Current (I) = Charge (Q) / Time (t) Unit: Ampere (coulomb/second) One Ampere of current flows through a wire if one coulomb of charge flows in one second at any section. 1.2 Electric Potential & Potential Difference Electric Potential: The charged body has capacity to do work by moving other charges either by attraction or by repulsion. This ability of the charged body to do work is called electric potential. Electric Potential (V) = Work Done / Charge = W (Joules) / Q (Coulombs) Unit: Volt (joule/coulomb) Potential Difference: The difference in the potentials of two charged bodies is called potential difference. 1.3 Resistance The opposition offered by a substance to the flow of electric current is called resistance. Unit: Ohm (Ω) Definition: A wire has resistance of 1 ohm if a potential difference of 1 volt across its ends causes 1 ampere to flow through it. Characteristics of resistance: Directly proportional to length of conductor Inversely proportional to cross-sectional area Depends on nature of material Depends on temperature Formula: Resistance (R) = ρl/A ohm Where: ρ = resistivity of material l = length A = cross-sectional area Uses: Voltage dividing, current limiting, etc. 1.4 Electric Power The rate at which work is done in an electric circuit is called electric power. Electric Power (P) = (Electrical energy consumed) / Time P = VI = I²R = V²/R Unit: Watt BEEE UNIT-1 DC CIRCUITS - Part 2: Inductors and Capacitors 1.5 Inductor An Inductor is a passive electrical component consisting of a coil of wire designed to take advantage of the relationship between magnetism and electricity as a result of electric current passing through the coil. Basic Form: Inductor is a coil of wire wound around a central core. For most coils, current (i) flowing through the coil produces magnetic flux (NΦ) proportional to the electrical current flow. Construction: Inductors are formed with wire tightly wrapped around a solid central core which can be: Straight cylindrical rod Continuous loop or ring to concentrate magnetic flux Types based on core: Hollow core (free air) Solid iron core Soft ferrite core Self-Induced EMF An inductor opposes the rate of change of current flowing through it due to build up of self-induced emf. Inductors resist or oppose changes of current but will easily pass steady state DC current. Self-induced voltage: e = -L(dΦ/dt) = -L(di/dt) Inductance Formula: L = μN²A/l Where: N = number of turns A = cross-sectional area (m²) Φ = amount of flux in Webers μ = permeability of core material l = length of coil (meters) di/dt = current’s rate of change (amps/second) Flux Linkage Relationship: NΦ = Li Unit: Henry (H) 1.6 Capacitors A capacitor consists of two conducting surfaces separated by a layer of insulating medium called dielectric. The dielectric can be paper, glass, ceramic, air, etc. Capacitance is the electrical property of a capacitor and is the measure of ability to store electric charge. Definition: Capacitance may be defined as the amount of charge required to create unit potential difference between its plates. C = Q/V = Coulombs/Volts Unit: 1 Farad = 1 Coulomb/Volt Physical Formula: C = εA/d Where: ε = permittivity of dielectric medium A = area of one plate d = separation between plates Properties: Capacitance is proportional to plate area (A) Capacitance is inversely proportional to separation between plates (d) BEEE UNIT-1 DC CIRCUITS - Part 3: Voltage and Current Sources 1.7 Voltage and Current Sources Ideal Voltage Source A voltage source whose output voltage remains constant irrespective of the change in load current. Characteristics: Zero internal resistance Constant output voltage regardless of load current Not practically achievable (every real source has some internal resistance) Smaller the internal resistance, closer it approaches ideal behavior Ideal Current Source A current source whose output current remains constant irrespective of the change in load resistance. Characteristics: Infinite internal resistance Constant output current at any load resistance In practice, has very high resistance Higher the internal resistance, closer it approaches ideal behavior Source Transformation Case (i): Voltage Source to Current Source A voltage source with series resistance can be converted into an equivalent current source with parallel resistance. Conversion Formula: I = V/R Key Point: If polarity of voltage source changes, the direction of equivalent current source also changes. Case (ii): Current Source to Voltage Source A current source with parallel resistance can be converted into an equivalent voltage source with series resistance. Conversion Formula: V = IR Key Point: If direction of current source changes, the polarity of equivalent voltage source also changes. Examples of Source Transformation: Example 1: 10V source in series with 5Ω → 2A source in parallel with 5Ω Example 2: 27V source in series with 9Ω → 3A source in parallel with 9Ω Example 3: 4A source in parallel with 5Ω → 20V source in series with 5Ω Example 4: 2A source in parallel with 10Ω → 20V source in series with 10Ω Important Notes: The resistance value remains the same in both equivalent circuits Only the configuration (series/parallel) and source type (voltage/current) changes Source transformation is a powerful tool for circuit simplification The equivalent circuits produce the same voltage and current at the terminals BEEE UNIT-1 DC CIRCUITS - Part 4: Kirchhoff’s Laws 1.8 Kirchhoff’s Laws These laws are used for solving electrical networks. Kirchhoff’s laws are particularly useful for: Determining equivalent resistance of complicated networks Calculating currents flowing in various conductors Kirchhoff’s Current Law (KCL) Statement: In any electrical network, the algebraic sum of the currents meeting at a point (or junction) is zero. Mathematical Expression: ΣI = 0 (at a junction) Physical Meaning: Total current leaving a junction = Total current entering that junction Based on principle: no accumulation of charge at junction Incoming currents = positive, outgoing currents = negative Example: I₁ + I₄ = I₂ + I₃ + I₅ or I₁ + (-I₂) + (-I₃) + I₄ + (-I₅) = 0 Kirchhoff’s Voltage Law (KVL) Statement: The algebraic sum of the products of currents and resistances in each of the conductors in any closed path (or mesh) in a network plus the algebraic sum of the e.m.f.s in that path is zero. Mathematical Expression: ΣIR + Σemf = 0 (around a mesh) Sign Conventions for KVL Voltage Signs: Rise in potential = positive Fall in potential = negative EMF Signs: Going from negative to positive terminal = positive (rise in potential) Going from positive to negative terminal = negative (fall in potential) Resistance Voltage Drop Signs: Going in same direction as current = negative (fall in potential) Going opposite to current direction = positive (rise in potential) Voltage Drop Formula: Going with current: Voltage drop = -I₁R₁ Going against current: Voltage drop = +I₁R₁ Key Points: KCL is based on conservation of charge KVL is based on conservation of energy Sign conventions are crucial for correct results These laws form the foundation for all circuit analysis methods Can be applied to any linear bilateral network BEEE UNIT-1 DC CIRCUITS - Part 5: Series Circuits 1.9 DC Circuits The closed path followed by direct current (dc) is called a dc circuit. DC Circuit Classifications: Series Circuit Parallel Circuit Series-Parallel Circuit 1.9.1 Series Circuit The circuit in which resistances are connected end to end so that there is only one path for current flow. Key Characteristics: Same current flows through each resistance Applied voltage equals sum of different voltage drops Total power consumed equals sum of powers consumed by individual resistances Every resistor has its own voltage drop Analysis of Series Circuit By Ohm’s Law: Voltage drop across R₁: V₁ = IR₁ Voltage drop across R₂: V₂ = IR₂ Voltage drop across R₃: V₃ = IR₃ Total Voltage: V = V₁ + V₂ + V₃ = IR₁ + IR₂ + IR₃ = I(R₁ + R₂ + R₃) Total Resistance: R = V/I = R₁ + R₂ + R₃ General Formula for Series Resistance: R_total = R₁ + R₂ + R₃ + ... + Rₙ Voltage Divider Rule A series circuit acts as voltage divider as it divides the total supply voltage into different voltages across circuit elements. For two resistors R₁ and R₂: V₁ = V_in × R₁/(R₁ + R₂) V₂ = V_in × R₂/(R₁ + R₂) Derivation: Total current: I = V_in/(R₁ + R₂) Voltage across R₁: V₁ = IR₁ = V_in × R₁/(R₁ + R₂) Voltage across R₂: V₂ = IR₂ = V_in × R₂/(R₁ + R₂) Series Circuit Properties Summary: Current: Same through all components Voltage: Divides proportionally to resistance values Resistance: Adds up algebraically Power: Individual powers add up to total power Application: Voltage dividers, current limiting circuits Practical Applications: Voltage dividers in electronic circuits Current limiting resistors Series connected batteries Christmas lights (traditional) BEEE UNIT-1 DC CIRCUITS - Part 6: Parallel Circuits 1.9.2 Parallel Circuit The circuit in which one end of each resistance is joined to a common point and the other end of each resistance is joined to another common point, so that there are as many paths for current flow as the number of resistances. Key Characteristics: Voltage drop across each resistance is same Total current equals sum of branch currents Total power consumed equals sum of powers consumed by individual resistances Every resistor has its own current Analysis of Parallel Circuit Consider three resistances R₁, R₂, and R₃ connected in parallel across battery of V volts: Current through each branch: Current through R₁: I₁ = V/R₁ Current through R₂: I₂ = V/R₂ Current through R₃: I₃ = V/R₃ Total Current: I = I₁ + I₂ + I₃ = V/R₁ + V/R₂ + V/R₃ = V(1/R₁ + 1/R₂ + 1/R₃) Total Resistance: From I = V/R_total, we get: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ General Formula for Parallel Resistance: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/Rₙ Current Divider Rule A parallel circuit acts as current divider as it divides the total circuit current in all branches. For two resistors R₁ and R₂: I₁ = I_total × R₂/(R₁ + R₂) I₂ = I_total × R₁/(R₁ + R₂) Note: Current divides inversely proportional to resistance values. Derivation: Equivalent resistance: R = R₁R₂/(R₁ + R₂) Total current: I = V/R = V(R₁ + R₂)/(R₁R₂) Since V = I₁R₁ = I₂R₂ Therefore: I₁ = I × R₂/(R₁ + R₂) And: I₂ = I × R₁/(R₁ + R₂) Parallel Circuit Properties Summary: Voltage: Same across all components Current: Divides inversely proportional to resistance values Resistance: Reciprocal of total equals sum of reciprocals Power: Individual powers add up to total power Advantage: If one component fails, others continue to work Practical Applications: Household electrical wiring Current dividers Parallel connected batteries Electronic circuit branches BEEE UNIT-1 DC CIRCUITS - Part 7: Network Terminology and Mesh Analysis 1.10 Network Terminology Node: Point in network where two or more circuit elements meet together. Junction: Point in network where three or more branches meet together. Loop: Any closed path through a circuit where no node is encountered more than once. Mesh: A closed path through a circuit with no other paths inside it. A mesh is also a loop but a loop may or may not be a mesh. Branch: Any single element (like resistor, voltage source) or series combination of elements between two nodes. 1.11 Maxwell’s Mesh Current Method This method applies Kirchhoff’s voltage law to each mesh in terms of mesh currents instead of branch currents. Key Concepts: Each mesh is assigned a separate mesh current Mesh current flows in clockwise direction around perimeter of mesh Mesh current doesn’t split at junctions into branch currents Mesh currents are fictitious quantities (cannot be measured directly) Branch currents are real currents (can be measured) Steps for Mesh Analysis: Step 1: Assign separate mesh current to each mesh (assume clockwise direction) Step 2: Express branch currents in terms of mesh currents: If two mesh currents flow through same element, actual current is algebraic sum Example: Current through common element = (I₁ - I₂) or (I₂ - I₁) depending on direction Step 3: Apply Kirchhoff’s voltage law to write equation for each mesh Step 4: Solve resulting system of linear equations for mesh currents Step 5: Calculate branch currents from mesh currents Example Mesh Equations: For two-mesh circuit: Mesh 1: I₁(R₁ + R₂) - I₂R₂ = E₁ Mesh 2: -I₁R₂ + I₂(R₂ + R₃) = -E₂ General Form: -I₁R₁ - (I₁ - I₂)R₂ + E₁ = 0 -I₂R₃ - (I₂ - I₁)R₂ - E₂ = 0 Important Notes: If mesh current comes out negative, actual direction is anticlockwise Mesh analysis is particularly useful for circuits with many loops Number of equations = Number of independent meshes Mesh currents are mathematical tools for analysis BEEE UNIT-1 DC CIRCUITS - Part 8: Nodal Analysis (Node Voltage Method) 1.11 Nodal Analysis This method is based on Kirchhoff’s current law (KCL). Analysis is carried out to determine voltages of different nodes with respect to reference node. Advantages: Useful when number of loops is large (mesh analysis becomes lengthy) Minimum number of equations need to be written After finding node voltages, all branch currents can be determined Steps for Nodal Analysis: Step I: Mark all nodes Every junction where three or more branches meet is a node Combine nodes that are connected by short circuits Step II: Select reference node Choose node where maximum elements are connected Also called zero potential node, datum node, or ground node Usually assigned 0V potential Step III: Assign unknown potentials Assign unknown voltages (V₁, V₂, etc.) to all nodes except reference node All voltages measured with respect to reference node Step IV: Assume current directions At each non-reference node, assume unknown currents Mark their directions arbitrarily Step V: Apply KCL at each node Write equations in terms of node voltages Solve the system of equations for node voltages Calculate branch currents from node voltages General Node Equation Form: At node with voltage V₁: (V_source - V₁)/R₁ = (V₁ - 0)/R₂ + (V₁ - V₂)/R₃ At node with voltage V₂: (V₁ - V₂)/R₃ = (V₂ - 0)/R₄ + (V₂ - (-V_source))/R₅ Example Applications: Type I: Simple circuit with voltage sources only Apply KCL directly at each node Express currents using Ohm’s law: I = V/R Type II: Circuits with current sources Current sources contribute directly to KCL equations Voltage sources converted to current sources if needed Key Points: Number of equations = (Number of nodes - 1) Reference node reduces number of unknowns by 1 Particularly efficient for circuits with few nodes but many loops Node voltages are real, measurable quantities BEEE UNIT-1 DC CIRCUITS - Part 9: Superposition Theorem 1.11 Superposition Theorem Applicable for linear and bilateral networks. If there are multiple sources acting simultaneously in any linear bilateral network, then each source acts independently of the others. Statement In a linear network containing more than one source, the resultant current in any branch is the algebraic sum of the currents that would be produced by each source acting alone, all other sources of emf being replaced by their respective internal resistances. Mathematical Expression I_total = I_due_to_source1 + I_due_to_source2 + ... + I_due_to_sourceN Steps to Apply Superposition Theorem: Step 1: Consider one source acting alone Replace all other voltage sources with short circuits Replace all other current sources with open circuits Calculate current/voltage in the desired branch Step 2: Repeat for each source individually Each time, only one source is active All others replaced by their internal resistances Step 3: Algebraically add all individual contributions I_AB = I_AB(due to V₁) + I_AB(due to V₂) + I_AB(due to I₁) + ... Source Replacement Rules: Ideal voltage source → Short circuit (0Ω) Ideal current source → Open circuit (∞Ω) Real voltage source → Replace with internal resistance Real current source → Replace with internal resistance Example Analysis Process: Case (i): V₁ acting alone Replace V₂ with short circuit Calculate current I_AB1 using any method (Ohm’s law, voltage division, etc.) Case (ii): V₂ acting alone Replace V₁ with short circuit Calculate current I_AB2 using any method Case (iii): Superposition I_AB(total) = I_AB1 + I_AB2 Important Notes: Only applicable to linear circuits Sources must be independent Algebraic addition means considering signs (directions) Power cannot be calculated using superposition (power is not linear) Useful for circuits with multiple sources Each source analysis is simpler than analyzing complete circuit BEEE UNIT-1 DC CIRCUITS - Part 10: Thevenin’s Theorem 1.12 Thevenin’s Theorem Powerful tool to simplify complex problems and obtain circuit solutions quickly. Reduces complex circuit to simple circuit. Particularly useful to find current in a particular branch when that branch resistance varies while all other resistances and sources remain constant. Developed by: French engineer M.L. Thevenin in 1883. Statement Any two terminal networks, however complex, can be replaced by a single source of emf V_TH (called Thevenin voltage) in series with a single resistance R_TH (called Thevenin resistance). Thevenin Parameters: V_TH (Thevenin Voltage): Open circuit voltage across terminals A and B with load removed Voltage that appears across load terminals when no load is connected R_TH (Thevenin Resistance): Resistance obtained with load removed Looking back into terminals A and B when all sources replaced by internal resistances For ideal sources: voltage sources → short circuit, current sources → open circuit Thevenin Equivalent Circuit I_L = V_TH/(R_TH + R_L) Steps to Apply Thevenin’s Theorem: Step 1: Remove the branch resistance (load) through which current is to be calculated Step 2: Calculate V_TH Find voltage across open-circuited terminals Use any network simplification technique (mesh analysis, nodal analysis, etc.) Step 3: Calculate R_TH Remove load resistance Replace all voltage sources with short circuits Replace all current sources with open circuits Find equivalent resistance across load terminals Step 4: Draw Thevenin equivalent circuit Show voltage source V_TH in series with resistance R_TH Step 5: Reconnect load resistance R_L Calculate load current using: I_L = V_TH/(R_TH + R_L) Key Advantages: Simplifies complex circuit analysis Useful when load resistance varies Reduces calculation time Makes circuit behavior clearer Helps in impedance matching applications Applications: Electronic circuit desi

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I havent given the book a try yet, it sounds good and intresting but it hasnt really captured my full attention. What caught my attention was the cover because thats a picture from Voltage Inc stories. The picture belongs to one of their stories called “My last first kiss” which i totally recommend, only thing is that youve gotta buy the stories for each character.

Just was thinking - at last an author which doesn't write about things which has no idea what exactly are they and suddenly -BAM - the author decide to invent a "flying disk"! Why? Because 100 years ago the people couldn't fly at all but then they invented the airplanes. Of course such small details as the airplanes mimicking the flight of the birds... who cares... Neither he cares about the fact the airplanes and the choppers fly due to the Bernoulli's principle. Neither the author has the slightest idea it is not the electricity voltage which is dangerous and harmful for the humans but the strength of the electric current (the amperes). There were cases where just the measly 42 Volts killed humans.