Electronics Application in Agriculture PDT 182 I will

Electronics Application in Agriculture PDT 182

I will care for myself & others n I will be ON TIME n I will be respectful at all times I will be a responsible student & listener n I will cooperate & be fair n I will always do my best n n

LET’S GET TO KNOW THIS COURSE

Chapter 1 Basic Concepts of Electrical Circuit

Introduction n Basic concepts and Basic circuit element: q q q n Charge & Current Branch, Node & Loop Y and Delta circuit Revision on: q q q Energy / Power conservation’s Law Ohm’s Law Kirchhoff’s Law. Voltage & Current Divider Rules Y and Delta circuit transformation technique

What is Charge? Charge The unit of charge is the coulomb (C) where one coulomb is one ampere second. [1 C = 1 A・s] (1 Coulomb = 6. 24 x 1018 electrons). The coulomb is defined as the quantity of electricity which flows pass a given point in an electric circuit when a current of one ampere is maintained for one second. Thus, charge, in coulombs Q = I x t where I is the current in amperes and t is the time in seconds.

Example 1 If a current of 5 A flows for 2 minutes, find the quantity of electricity transferred. Answer :

What is Current? Electric current means, a flow of electric charge or more specific, the rate of flow of electric charge (a quantity of electron). This flowing electric charge is typically carried by moving electrons, in a conductor such as wire. The SI unit for measuring the rate of flow of electric charge is the ampere, which is charge flowing at the rate of one coulomb per second. Electric current is measured using an ammeter. Charge, Q = I x t [C] Thus, Current, I = Q / t [A] Higher current value means that more quantity of charge (electrons) are flowing in a second.

1 st Law – Ohm’s Law Ohm’s law states that the current I flowing in a circuit is directly proportional to the applied voltage V and inversely proportional to the resistance R, provided the temperature remains constant. Thus, OHM’S LAW says, if the source voltage remains constant, increasing the resistance in a circuit will cause a decrease in current flow in that circuit. In mathematical terms it tells us that current flow is inversely proportional to resistance.

Law of Conservation Law of conservation power: total power supplied to the circuit must balance the total power absorbed. Passive sign convention is satisfied when the current enters through the positive terminal of an element and p= +vi. If the current enters through the negative terminal, p= － vi.

Branches, Nodes & Loops • • • Branch represents a single elements such as a voltage source or resistor. A branch represents any twoterminal element. Node is the point of connection between two or more branches. It usually indicated by a dot in a circuit. Loop is any closed path in a circuit ; 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. Branch Node Loop

Example 2 q Determine how many branches and nodes for the following circuit.

Solution q Determine how many branches and nodes for the following circuit.

Kirchhoff’s Law • First introduced in 1874 by the German physicist Gustav Robert Kirchhoff (1824 -1887) • Divided into two : • Kirchhoff’s current law (KCL) • Kirchhoff’s voltage law (KVL) • Kirchhoff’s laws known as Kirchhoff’s Current Law (KCL) and Kirchhoff’s Voltage Law (KVL) are based respectively on the conservation of charge and the conservation of energy. They along with Ohm’s law present the fundamental tools for circuit analysis.

Kirchhoff’s Current Law Kirchhoff’s current law (KCL): 1. The algebraic sum of currents entering a node (or close boundary) is zero. 2. The sum of the currents entering a node is equal to the sum of the currents leaving the node. i 5 i 1 i 3 i 2 i 4 Fig: Currents at a node illustrating KCL Current entering node = +ve Current leaving node = - ve

Exercise 3 q Use KCL to obtain currents i 1, i 2, and i 3 in the circuit.

Kirchhoff’s Voltage Law Kirchhoff’s voltage law (KVL): 1. The algebraic sum of all voltages around a closed path (or loop) is zero. 2. Sum of voltage drops is equal to sum of voltage rises. + v 2 - v 1 + v 3 - + - - v 4 + - v 5 + Sum of voltage drop = Sum of voltage rises

Exercise 4 q Use KVL to obtain v 1, and v 2.

Series Resistors and Voltage Divider Rule Consider a single-loop circuit with two resistors in series i v • a + v 1 - + v 2 - R 1 R 2 Applying Ohm’s law of each resistor (1) + - If apply KVL to the loop, we have b (2) • i v • a +v - Combining (1) and (2): or Req + b Voltage Divider Rule : For ex.

Series Resistors and Voltage Divider The equivalent resistance Rule of any number of resistors connected in series is the sum of the individual resistances. Mathematically, To determine the voltage across each resistor shown in below figure, • a Principle of voltage division: v + b • + v 1 - + v 2 - R 1 R 2

Parallel Resistors and Current Divider Rule Consider the circuit below where two resistors are connected in parallel and therefore have the same voltage across them. From Ohm’s law i Node a i 2 i 1 v + - R 1 (1) R 2 Applying KCL at node a, gives (2) Node b Substitute (1) into (2), we get For a circuit with N resistors in parallel,

Parallel Resistors and Current Divider Rule The equivalent resistance of two parallel resistors is equal to the product of their resistances divided by their sum. Mathematically, For a circuit with N resistors in parallel : In parallel connection, equivalence conductance, Geq Current Divider Rule : Unit for Conductance, G is Siemens [S]

Parallel Resistors and Current Divider Rule For the special case of 2 resistors connected in parallel, current through resistor R 1 and R 2 can be calculated by following formula.

Delta ( ) circuit Definition A delta (or mesh) connected load is three loads where the end of one load is connected to the start of the next load.

Wye (Y) circuit Definition A Y (or star)-connected load is a circuit where three line conductors are each connected to a load and the outlets from the loads are joined together at N to form what is termed the neutral point. N point

Y - Circuit Transformation Y to conversion: each resistor in the network is the sum of all possible products of Y resistors taken two at a time, divided by the opposite Y resistor.

- Y Circuit Transformation

Exercise 7 q Transform the circuit from Δ to y.

Exercise 8 Use Kirchhoff’s laws (KCL, KVL) to determine the currents flowing in each branch of the network shown in below figure.

i 1 i 2 i 3 Answer