Electrical Circuits & Machines: Basics and Analysis Techniques

ELECTRICAL CIRCUITS AND MACHINES Teaching Scheme: Examination Scheme: Lectures: 3hrs/week Online: 50 marks Practical: 2hrs/week End Sem: 50 marks Term work: 25 marks Credits:4 Prof. A R Suryawanshi, PCCOE

Prerequisite for Unit I Students should have the knowledge of basic electrical concepts such as voltage, current, power, ac signal, dc signal, etc; Properties of Resistor, Capacitor, Inductor Basic Mathematical concepts such as Cramer's rule, Polar to rectangular conversion & vice versa. Prof. A R Suryawanshi, PCCOE

Basic Circuit Analysis and Simplification Techniques: Unit I 1.1 Kirchhoff’s Current and Voltage Laws, Independent and dependent sources and their interconnection, and power calculations. 1.2 Network Analysis: Mesh, Super mesh, Node and Super Node analysis. Source transformation and Source shifting. 1.3 Network Theorems: Superposition Theorem, Thevenin’s Theorem, Norton’s Theorem, Maximum Power -Transfer Theorem, Millers Theorem and its dual. Prof. A R Suryawanshi, PCCOE

Electrical Networks Vs Electrical Circuits An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources, andswitches. An electrical circuit is a network that has a closed loop, giving a return path for the current. A network is a connection of two or more components, and may notnecessarily be a circuit. Prof. A R Suryawanshi, PCCOE

Continued… Is it Network or Circuit? Prof. A R Suryawanshi, PCCOE

Continued… That means all circuits can be networks but all networks cannot be circuits Prof. A R Suryawanshi, PCCOE

Basic concepts of network theory … Circuit Element: Any individual circuit component like inductor, resistor, capacitor, generator with two terminals. 2. Branch: A group of circuit elements usually in series and with two terminals. Network and Circuit: An electric network is any possible interconnection of electric circuit elements and branches. An electric circuit is closed energized network. A network is not necessarily a circuit. e.g. T network. Lumped Network: A network in which physically separate resistors, capacitors, inductors are present. Prof. A R Suryawanshi, PCCOE

Basic concepts of network theory … 5. Distributed network: In this network, resistors, capacitors and inductors cannot be electrically separated and individually isolated as separate elements. e.g. Transmission line. 6. Linear Network: A network for which the principle of superposition holds. 7. Mesh and Loop: A set of branches forming a closed path such that removal of any branch makes it open. Mesh must not have any other closed circuit inside it. Loop may have other loops or meshes inside it. 8. Node or Junction: A terminal of any branch of a network common to two or more branches is known as a node. Prof. A R Suryawanshi, PCCOE

Electricity basics...... Voltage, Current, Resistance and Ohm's Law Georg Ohm Prof. A R Suryawanshi, PCCOE

Ohms Law Combining the elements of voltage, current, and resistance, Ohm developed the formula: V = I . R Where V = Voltage in volts I = Current in amps R = Resistance in ohms This is called Ohm’s law. Let’s say, for example, that we have a circuit with the potential of 1 volt, a current of 1 amp, and resistance of 1 ohm. Using Ohm’s Law we can say: 1V = 1A. 1Ω Prof. A R Suryawanshi, PCCOE

Ohms Law The statement of Ohm’s law is simple, and it says that whenever a potential difference or voltage is applied across a resistor of a closed circuit, current starts flowing through it. This current is directly proportional to the voltage applied if temperature and all other factors remain constant. Thus we can mathematically express it as: V α I Prof. A R Suryawanshi, PCCOE

Ohm’s Law Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Kirchhoff’s Voltage Law (KVL): The algebraic sum of all branch voltages around any closed loop of a network is zero at all instants of time. Kirchhoff’s Current Law (KCL): The algebraic sum of branch currents at anode is zero at all instants of time. Gustav Kirchhoff Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Sources of Electrical Energy: Independent Sources: The value of the source quantity is not affected by current or voltage quantities in remainder circuit. Ideal Voltage Source: An ideal voltage source is a two terminal element which maintains a terminal voltage v(t) regardless of the value of the current through its terminals. Practical Voltage Source: In a practical voltage source, the voltage across terminals of the source reduces as current through it increases. This behaviour can be represented by putting a resistance in series with an ideal voltage source. Ideal Voltage Source Practical Voltage Source Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Ideal Current Source: An ideal current source is a two terminal elements which maintains a current i(t) flowing through its terminals regardless of the value of the terminal voltage. Practical Current Source: In a practical current source the current through the source decreases as the voltage across it increases. Ideal Current Source Practical Current Source Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Controlled or Dependent Sources: The source quantity is determined by a current or voltage existing at some other location in the system/circuit being analysed. Types of Dependent or Controlled Sources: 1. Voltage controlled voltage source (VCVS) 2. Current controlled voltage source (CCVS) 3. Voltage controlled current source (VCCS) 4. Current controlled current source (CCCS) Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Source Transformation and Source Shifting: a) Current source and its equivalent voltage source Current-Source to Voltage-Source Transformation Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques b) Voltage Source and its equivalent current source Voltage -Source to Carrent – Source Transformation Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques c) Equivalent of two voltage sources in series Voltage Sources in Series Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques e) Equivalent current and voltage sources from mixed source Mixed Sources Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques f) Transformation of voltage sources without resistance Voltage - Source Shifting Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques g) Current source with no parallel resistance Current - Source Shifting Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Series parallel equivalent of R, L, C, V & I Series Equivalent:- Resistors The total resistance of resistors in series is equal to the sum of their individual resistances: Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Series parallel equivalent of R, L, C, V & I Inductors: Inductors follow the same law, in that the total inductance of non-coupled inductors in series is equal to the sum of their individual inductances: Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Series parallel equivalent of R, L, C, V & I Capacitors: Capacitors follow the same law using the reciprocals. The total capacitance of capacitors in series is equal to the reciprocal of the sum of the reciprocals of their individual capacitances: Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Series parallel equivalent of R, L, C, V & I Voltages: Cells and batteries: A battery is a collection of electrochemical cells. If the cells are connected in series, the voltage of the battery will be the sum of the cell voltages. For example, a 12 volt car battery contains six 2-volt cells connected in series. Some vehicles, such as trucks, have two 12 volt batteries in series to feed the 24 volt system. Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Series parallel equivalent of R, L, C, V & I Current: In a series circuit the current is the same for all of elements. Parallel equivalent: Resistors: To find the total resistance of all components, add the reciprocals of the resistances of each component and take the reciprocal of the sum. Total resistance will always be less than the value of the smallest resistance: For only two resistors, the unreciprocated expression is reasonably simple: Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Series parallel equivalent of R, L, C, V & I Inductors: Inductors follow the same law, in that the total inductance of non-coupled inductors in parallel is equal to the reciprocal of the sum of the reciprocals of their individual inductances: Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Series parallel equivalent of R, L, C, V & I Capacitors: The total capacitance of capacitors in parallel is equal to the sum of their individual capacitances: Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques • Voltage division rule: • Current division rule: • Star to Delta and Delta to star conversions: Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Series parallel equivalent of R, L, C, V & I Voltage: If two or more components are connected in parallel they have the same potential difference (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applicable to all circuit components connected in parallel. The total current is the sum of the currents through the individual components, in accordance with Kirchhoff's current law. In a parallel circuit the voltage is the same for all elements. Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Series parallel equivalent of R, L, C, V & I Current: The current in each individual resistor is found by Ohm’s law. Factoring out the voltage gives For Current sources: Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Mesh Current Analysis Method: Basis of Mesh Current Analysis Method is Kirchhoff’s voltage law (KVL). Steps : 1. Determine no of meshes in the circuit. 2. Mark arbitrarily current directions for each mesh. 3. Apply KVL to each loop. 4. No of equations =No of Meshes. 5. Solve the equations simultaneously to determine Mesh currents. 6. From mesh currents determine branch currents and node voltages. Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Mesh Current Analysis Method: Basis of Mesh Current Analysis Method is Kirchhoff’s voltage law (KVL). Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Node Voltage Analysis Method: Basis of Node Voltage Analysis Method is Kirchhoff’s Current Law. Steps : 1. Simplify the circuit by combining impedances in parallel or series and combining current sources in parallel. 2. Determine number of nodes in the circuit. 3. Choose reference or datum node at zero potential. 4. Mark potentials at nodes as V1,V2,V3……. VN. 5. Mark branch currents in arbitrary directions. 6. Apply Kirchhoff’s current law at each node. 7. No. of equations=No. of nodes - 1 8. Solve the equations simultaneously to obtain unknown node voltages. 9. From node voltages determine branch currents. Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Super mesh and Super node: (a) Super mesh: Super mesh is formed when two meshes have current source as a common element, this means that the current source is in the interior of the super mesh. Reduce the number of meshes by 1 for each current source present. If the current source lies on the perimeter of circuit, then single mesh in which it is found, is ignored. Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques (b) Super node: Super node is formed by two nodes separated by voltage source with no series resistor. The KCL is applied to both the two nodes at the same time. Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Network Theorems: Though the techniques of nodal and mesh analysis are reliable and extremely powerful methods, both require a complete set of equations to describe a particular circuit, even if only one current, voltage, or power quantity is of interest. The theorems to be considered in detail include the superposition theorem, Thevenin’s & Norton's theorem, maximum power-transfer theorem, Millers Theorem & its dual. Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Definitions: Linear Element: A linear element is a passive element that has a linear voltage-current relationship i.e. Multiplication of the current through the element by a constant K results in the multiplication of the voltage across the element by the same constant K. for e.g. In case of a resistor v(t) = R i(t) is clearly linear i.e. If v(t) is plotted as a function of i (t), the result is a straight line. Bilateral Element: A bilateral network is one whose properties or characteristics are same in either direction. For example, a transmission line is a bilateral network, because it can be made to perform the function equally well in either direction. Conduction of current in both directions in an element (example: Resistance; Inductance; Capacitance) with same magnitude is termed as bilateral element. Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques A. Superposition Theorem: In any linear network containing bilateral linear impedances and energy sources, the current flowing in any element is the vector sum of the currents that are separately caused to flow in that element by each energy source. The principle of superposition states that the response (desired current or voltage) in a linear bilateral circuit having more than one independent source can be obtained by adding the responses caused by the separate independent sources acting alone. Procedure: Fundamental Concept: Look at each independent source one at a time with the other independent sources “turned off” or “zeroed out” or “deactivated”. The reason behind zeroing out the sources is that it leads to the simplest circuit. Dependent sources are in general active during analysis. {Pl note: Dependent sources are not sources of energy i.e. if all independent sources are removed from a system, all currents and voltages must be zero.} Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques Superposition Theorem: Example: Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques B. Thevenin’s Theorem : Any two-terminal linear bilateral network can be replaced by an equivalent circuit consisting of a voltage source and an impedance (resistor for dc circuit) in series. Thevenin’s theorem: Any two- terminal linear n/w containing energy sources and impedances can be replaced with an equivalent circuit consisting of a voltage source Voc or VTH in series with an impedance Ƶth, where the value of Voc is open circuit voltage between terminals of the network and Ƶth is the impedances measured between the terminals of the network with all energy sources eliminated (but not their impedances). *If dependent sources are also present along with Independent sources then Ƶth = Voc / ISC ;So need to calculate ISC Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques B. Thevenin’s Theorem : Example: Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques C. Norton’s Theorem : Any two-terminal linear bilateral network can be replaced by an equivalent circuit consisting of a current source and an impedance (resistor for dc circuit) in parallel. Norton’s theorem: Any two- terminal linear n/w containing energy sources and impedances can be replaced with an equivalent circuit consisting of a current source ISC or IN in parallel with an impedance Ƶ, where the value of ISC is short circuit current between terminals of the network and Ƶ is the impedances measured between the terminals of the network with all energy sources eliminated (but not their impedances). *If dependent sources are also present along with Independent sources then Ƶth = Voc / ISC So need to calculate Voc Prof. A R Suryawanshi, PCCOE

Basic Circuit Simplification Techniques C. Norton’s Theorem : Example: Prof. A R Suryawanshi, PCCOE

Electrical Circuits & Machines: Basics and Analysis Techniques