Linear Circuit Analysis: Understanding Ohm's Law and Kirchhoff's Laws, Slides of Engineering Physics

Download Linear Circuit Analysis: Understanding Ohm's Law and Kirchhoff's Laws and more Slides Engineering Physics in PDF only on Docsity! LINEAR CIRCUIT ANALYSIS (EED) – U.E.T. TAXILA 02 ENGR. M. MANSOOR ASHRAF INTRODUCTION To actually determine the values of voltage or current of elements in given circuit, requires study of basic laws. The basic laws: Ohm’s law and Kirchhoff’s laws, form the foundation of electric circuit analysis. In addition to these laws, some techniques are applied for circuit design and analysis. These techniques includes combining resistors in series or parallel, voltage division, current division, and delta-to- wye and wye-to-delta transformations. OHM’S LAW Ohm’s Law states that the voltage across a resistor is directly proportional to the current flowing through the resistor. Mathematically; Where ‘R’ is known as resistance of element (Resistor). RESISTANCE Materials in general have a characteristic behavior of resisting the flow of electric charge. This physical property, or ability to resist current, is known as resistance. The Resistance of an element denotes its ability to resist the flow of electric current, measured in ohms (Ω). Mathematically; FIXED RESISTOR Fixed Resistor is that which exhibits the constant value of resistance. There are two common types of fixed resistors: wire wound and composition. The wire wound resistors are used for large values of resistance. VARIABLE RESISTOR Variable Resistor is that which exhibits adjustable value of resistance. The variable resistor is also known as Potentiometer. VALUE OF RESISTOR Since value of R can range from zero to infinity, it is important to consider extreme possible values of R. A Short Circuit is a circuit element with resistance approaching to zero. VALUE OF RESISTOR An Open Circuit is a circuit element with resistance approaching to infinity. LINEAR RESISTOR A resistor that obeys Ohm’s law is known as Linear Resistor. Its has a constant resistance and thus its current-voltage characteristic (i-v graph) is straight line passing through origin. NON-LINEAR RESISTOR A resistor that does not obey Ohm’s law is known as Non-Linear Resistor. Its resistance varies with current its current-voltage characteristic (i-v graph) is not straight line. NODE A Node is the point of connection between two or more branches. If a short circuit connects two nodes, the two nodes constitute a single node. LOOP A Loop is any closed path in a circuit. A loop is a closed path formed by starting at a node, passing through a set of nodes, and returning to the starting node without passing through any node more than once. A loop is said to be independent if it contains at least one branch which is not a part of any other loop. LOOP The loop abca with 2 Ω resistor and loop abca with 3 Ω resistor are examples of independent loops. A network with b branches, n nodes and l independent loops will satisfy the fundamental theorem of network topology. SERIES CONNECTED ELEMENTS Two or more elements are in Series if they exclusively share a single node and consequently carry the same current. Elements are in series when they are chain-connected. PARALLEL CONNECTED ELEMENTS Two or more elements are in Parallel if they are connected to same two nodes and consequently have the same voltage across them. Elements are in parallel when they are connected to same pair of nodes. PROBLEMS Determine number of branches and nodes in circuits? Also identify which elements are connected in series and parallel? KIRCHHOFF’S VOLTAGE LAW (KVL) The sign on each voltage is the polarity of the terminal encountered first as we travel around the loop. KIRCHHOFF’S VOLTAGE LAW (KVL) The application of KVL is combining the voltage sources. PROBLEMS Find the voltages v1 and v2? (8 V, -12 V) Find the current io and voltage vo? (6 A, 24 V) PROBLEMS Find currents and voltages in the circuit? (3 A, 2 A, 1 A, 24 V, 6 V, 6 V) SERIES RESISTORS AND VOLTAGE DIVISION Consider the series circuit; Applying Ohm’s law; Applying KVL; SERIES RESISTORS AND VOLTAGE DIVISION Voltages across each resistor; The equivalent resistance of any number of resistors connected in Series is the sum of their individual resistances. PROBLEMS Find equivalent resistance? (14.4 Ω) ( (6 Ω) PROBLEMS Find voltages and currents? (4 V, 4/3 A) (5 V, 10 V, 416.7 mA, 250 mA) WYE AND DELTA CONNECTED RESISTORS Sometimes, the resistors are neither in parallel connected nor in series. Such complex pattern of resistors is solved by considering them in wye or delta. DELTA-WYE TRANSFORMATION WYE-DELTA TRANSFORMATION RyRy + RoRs + RR, R a Ry a R, Ro + RoRz + R3R, rr 2 p= Rika + RoRs + RR Cc a R; PROBLEMS Find equivalent resistance? 30Q AAA WN (9.632 ohm)