FCI Gen One Physics Week 3 Lecture Notes PDF

Mansoura University Faculty of Computers and Information Department of Information Technology First Semester- 2021-2022 [UNI113P] Physics Grade: FIRST - GENERAL Dr. Nehal Sakr; Dr. Fatmaelzahraa Ahmed CHAPTER 3 BASIC LAWS 2 OUTLINE  Ohm’s Law  Nodes, Br...

Mansoura University Faculty of Computers and Information Department of Information Technology First Semester- 2021-2022 [UNI113P] Physics Grade: FIRST - GENERAL Dr. Nehal Sakr; Dr. Fatmaelzahraa Ahmed CHAPTER 3 BASIC LAWS 2 OUTLINE  Ohm’s Law  Nodes, Branches, and Loops  Kirchhoff ’s Laws 3 OHM’S LAW  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 (𝑅).  The resistance of any material can be obtained through: 𝓁 𝑅=𝜌 𝐴 Where: a uniform cross-sectional area 𝐴 depends on A and its length 𝓁, and 𝜌 is known as the resistivity of the material in ohm-meters.  Good conductors, such as copper and aluminum, have low resistivities, 4 while insulators, such as mica and paper, have high resistivities. OHM’S LAW (CONT.)  The circuit element used to model the current-resisting behavior of a material is the resistor.  Georg Simon Ohm (1787–1854), a German physicist, found the relationship between current and voltage for a resistor [Ohm’s law].  Ohm’s law states that the voltage 𝑣 across a resistor is directly proportional to the current 𝑖 flowing through the resistor.That is 𝑣 ∝ 𝑖.  Ohm defined the constant of proportionality for a resistor to be the resistance, 𝑅.  Accordingly, the mathematical form of Ohm’s law became: 𝑣 = 𝑖𝑅 Where R is measured in the unit of ohms, designated Ω.  Therefore, resistance 𝑅 of an element denotes its ability to resist the flow of electric current; it is measured in 𝑣 5 ohms (Ω). It can be represented through previous equation as: 𝑅 =. 𝑖 OHM’S LAW (CONT.)  To apply Ohm’s law, we must pay careful attention to the current direction and voltage polarity. Must conform with the passive sign convention. If the current flows from a higher potential to a lower potential, we will have 𝑣 = 𝑖𝑅. If the current flows from a lower potential to a higher potential, we will have 𝑣 = −𝑖𝑅.  Two special cases (two extreme possible values of 𝑅): 1. The resistance approaching zero: an element with 𝑅 = 0 is called a short circuit, and thus 𝑣 = 𝑖𝑅 = 0. Thus, a short circuit is a circuit element with resistance approaching zero. 𝑣 2. The resistance approaching infinity: an element with 𝑅 = ∞ is called a open circuit, and thus 𝑖 = lim = 0. 𝑅→∞ 𝑅 Thus, an open circuit is a circuit element with resistance approaching infinity. 6 OHM’S LAW (CONT.)  As previously mentioned, a resistor is either fixed or variable where most resistors are of the fixed type.  The two common types of fixed resistors (wirewound and composition) are shown in the figure where the composition resistors are used when large resistance is needed.  Variable resistors have adjustable resistance.A common variable resistor is known as a potentiometer or pot for short. 7 OHM’S LAW (CONT.)  Not all resistors obey Ohm’s law.  A resistor that obeys Ohm’s law is known as a linear resistor.  It has a constant resistance and its current-voltage characteristic is as:  A nonlinear resistor does not obey Ohm’s law.  Its resistance varies with current.  Its i-v characteristic is typically as: 8 OHM’S LAW (CONT.)  A useful quantity in circuit analysis is the reciprocal of resistance 𝑅, known as conductance and denoted by 𝐺 where: 1 𝑖 𝐺= = 𝑅 𝑣  The conductance is a measure of how well an element will conduct electric current, measured in mhos or reciprocal ohm (℧) or as in the SI, siemens (𝑆) where: 1 𝑆 = 1℧ = 1 𝐴Τ𝑉.  The same resistance can be expressed in ohms or siemens. For example, 10 Ω is the same as 0.1 𝑆. 9 OHM’S LAW (CONT.) 𝑖  Two notes: ∵𝐺= 𝑣 1. The power dissipated in a resistor is a nonlinear function of ∴ 𝑖 = 𝐺𝑣 either current or voltage.  The power dissipated by a resistor can be expressed in terms 2. Since 𝑅 and 𝐺 are positive quantities, the power dissipated in a of 𝑅 as: resistor is always positive. 𝑣 = 𝑖𝑅 Resistor always absorbs power from the circuit. 𝑣2 Confirms the idea that a resistor is a passive element, incapable 2 𝑝 = 𝑣𝑖 = 𝑖 𝑅 = of generating energy. 𝑅  The power dissipated by a resistor may also be expressed in terms of 𝐺 as: 2 𝑖2 𝑝 = 𝑣𝑖 = 𝑣 𝐺 = 𝐺 10 OHM’S LAW - PROBLEMS Example: In the circuit shown in the figure, calculate the current 𝒊, the conductance 𝑮, and the power 𝒑. Solution: For current 𝒊: The voltage across the resistor is the same as the source voltage (30 𝑉) because the resistor and the voltage source are connected to the same pair of terminals. Hence, the current is: 𝑣 30 𝑖= = = 6 𝑚𝐴 𝑅 5 × 103 For conductance 𝑮: 1 1 𝐺= = = 0.2 𝑚𝑆 𝑅 5 × 103 For power 𝒑: it can be calculated in different ways: 𝑝 = 𝑣𝑖 = 30 6 × 10−3 = 180 𝑚𝑊 ; Or 𝑝 = 𝑖 2 𝑅 = 6 × 10−3 2 5 × 103 = 180 𝑚𝑊 ; Or 𝑝 = 𝑣 2 𝐺 = 30 2 0.2 × 10−3 = 180 𝑚𝑊 11 NODES, BRANCHES, AND LOOPS  We need to understand some basic concepts of network topology.  To differentiate between a circuit and a network, we may regard: ▪ A network as an interconnection of elements or devices, whereas ▪ A circuit is a network providing one or more closed paths.  In network topology, we study the properties relating to the placement of elements in the network and the geometric configuration of the network. Such elements include branches, nodes, and loops. 12 NODES, BRANCHES, AND LOOPS (CONT.)  We need to understand some basic concepts of network topology.  To differentiate between a circuit and a network, we may regard: ▪ A network as an interconnection of elements or devices, whereas ▪ A circuit is a network providing one or more closed paths.  In network topology, we study the properties relating to the placement of elements in the network and the geometric configuration of the network. Such elements include branches, nodes, and loops. A branch represents a single element. OR any two-terminal element. 13 NODES, BRANCHES, AND LOOPS (CONT.)  We need to understand some basic concepts of network topology.  To differentiate between a circuit and a network, we may regard: ▪ A network as an interconnection of elements or devices, whereas ▪ A circuit is a network providing one or more closed paths.  In network topology, we study the properties relating to the placement of elements in the network and the geometric configuration of the network. Such elements include branches, nodes, and loops. A node is the point of connection between two or more branches. 14 Usually indicated by a dot in a circuit. NODES, BRANCHES, AND LOOPS (CONT.)  We need to understand some basic concepts of network topology.  To differentiate between a circuit and a network, we may regard: ▪ A network as an interconnection of elements or devices, whereas ▪ A circuit is a network providing one or more closed paths.  In network topology, we study the properties relating to the placement of elements in the network and the geometric configuration of the network. Such elements include branches, nodes, and loops. A loop is any closed path in a circuit.. starting at a node, passing through a set of nodes, and returning to the starting node without passing through any node more 15 than once.  NODES, BRANCHES, AND LOOPS (CONT.)  A network with 𝑏 branches, 𝑛 nodes, and 𝑙 independent loops will satisfy the fundamental theorem of network topology: 𝑏 = 𝑙 + 𝑛 − 1.  Important notes: 1. Two or more elements are series if they exclusively share a single node and consequently carry the same current. Chain-connected, connected sequentially, or end to end. 2. Two or more elements are parallel if they are connected to the same two nodes and consequently have the same voltage across them. 3. Elements may be connected in a way that they are neither in series nor in parallel.  NODES, BRANCHES, AND LOOPS - PROBLEMS Example: Determine the number of branches and nodes in the circuit shown in the figure. Identify which elements are in series and which are in parallel. Solution: Since there are four elements in the circuit, the circuit has four branches: 10 𝑉, 5 Ω, 6 Ω and 2 𝐴. The circuit has three nodes as identified in Figure 3.12. The 5 Ω resistor is in series with the 10 𝑉 voltage source because the same current would flow in both. The 6 Ω resistor is in parallel with the 2 𝐴 current source because both are connected to the same nodes 2 and 3. KIRCHHOFF’S LAWS  Ohm’s law by itself is not sufficient to analyze circuits.  However, when it is coupled with Kirchhoff’s two laws, we have a sufficient, powerful set of tools for analyzing a large variety of electric circuits.  Kirchhoff’s laws were first introduced in 1847 by the German physicist Gustav Robert Kirchhoff (1824–1887).  These laws are formally known as Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL). 19  KIRCHHOFF’S LAWS - KIRCHHOFF’S CURRENT LAW (KCL)  KCL is based on the law of conservation of charge, which requires that the algebraic sum of charges within a system cannot change.  KCL states that the algebraic sum of currents entering a node (or a closed boundary) is zero. By this law, currents entering a node may be regarded as positive, while currents leaving the node may be taken as negative or vice versa. The sum of the currents entering a node is equal to the sum of the currents leaving the node.  Mathematically, KCL implies that: 𝑁 ෍ 𝑖𝑛 = 0 𝑛=1 Where 𝑁 is the number of branches connected to the node and is the 𝑛th current entering (or leaving) the node. 𝑖1 + −𝑖2 + 𝑖3 + 𝑖4 + ሺ−𝑖 5 ) = 0 OR, 20 𝑖1 + 𝑖3 + 𝑖4 = 𝑖2 + 𝑖5  KIRCHHOFF’S LAWS - KIRCHHOFF’S CURRENT LAW (KCL) (CONT.)  A simple application of KCL is combining current sources in parallel.  Example: 𝐼𝑇 + 𝐼2 = 𝐼1 + 𝐼3 , OR 𝐼𝑇 = 𝐼1 − 𝐼2 + 𝐼3  Note: A circuit cannot contain two different currents, 𝐼1 and 𝐼2 , in series, unless 𝐼1 = 𝐼2 ; otherwise KCL will be violated. 21  KIRCHHOFF’S LAWS - KIRCHHOFF’S VOLTAGE LAW (KVL)  KVL is based on the principle of conservation of energy and it, KVL, states that the algebraic sum of all voltages around a closed path (or loop) is zero. 𝑆𝑢𝑚 𝑜𝑓 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑑𝑟𝑜𝑝𝑠 = 𝑆𝑢𝑚 𝑜𝑓 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑟𝑖𝑠𝑒𝑠  Mathematically, KVL implies that: 𝑀 ෍ 𝑣𝑚 = 0 𝑚=1 Where 𝑀 is the number of voltages in the loop (or the number of branches in the loop) and 𝑣𝑚 is the 𝑚th voltage. The sign on each voltage is the polarity of the terminal encountered first as we travel around the loop. Clockwise: −𝑣1 + 𝑣2 + 𝑣3 − 𝑣4 + 𝑣5 = 0, OR 𝑣2 + 𝑣3 + 𝑣5 = 𝑣1 + 𝑣4 Counterclockwise: +𝑣1 − 𝑣2 − 𝑣3 + 𝑣4 − 𝑣5 = 0 22  KIRCHHOFF’S LAWS - KIRCHHOFF’S VOLTAGE LAW (KVL) (CONT.)  When voltage sources are connected in series, KVL can be applied to obtain the total voltage.  Example: −𝑉𝑎𝑏 + 𝑉1 + 𝑉2 − 𝑉3 = 0, OR 𝑉𝑎𝑏 = 𝑉1 + 𝑉2 − 𝑉3 23  Note: To avoid violating KVL, a circuit cannot contain two different voltages 𝑉1 and 𝑉2 in parallel unless 𝑉1 = 𝑉2. KIRCHHOFF’S LAWS - PROBLEMS Example: For the circuit in the figure, find voltages 𝒗𝟏 and 𝒗𝟐. Solution: From Ohm’s law: 𝑣1 = 2𝑖, 𝑣2 = −3𝑖 (3.3.1) Applying KVL around the loop gives: −20 + 𝑣1 − 𝑣2 = 0 (3.3.2) Substituting Eq. (3.3.1) into Eq. (3.3.2), we obtain −20 + 2𝑖 + 3𝑖 = 0 or 5𝑖 = 20 ∴𝑖 =4𝐴 Substituting 𝑖 in Eq. (3.3.1) finally gives 𝑣1 = 8 𝑉, 𝑣2 = −12 𝑉 24 Thank you ☺ 25