Basic Concepts-v3-Annotated-EE101-A17.pptx

Module 1 – Part 1 Basic Concepts CIRCUITS 1 Cesar G. Manalo, Jr. Faculty, Department of Electrical Engineering  Basic Concepts Electric Circuit CIRCUITS 1...

Module 1 – Part 1 Basic Concepts CIRCUITS 1 Cesar G. Manalo, Jr. Faculty, Department of Electrical Engineering  Basic Concepts Electric Circuit CIRCUITS 1 Wire Battery Resistor Wire Simple electric circuit Schematic diagram of the electric circuit Is an interconnection of electrical elements linked together in a closed path so that an electric current may flow continuously.  Basic Concepts Charge and Current CIRCUITS 1 Charge (q or Q) Is an electrical (and intrinsic) property of the atomic particles of which matter consists, measured in coulombs (C). The charge of an electron is negative and equal in magnitude to C which is called as electronic charge. = -1 C of charge = electrons A unique feature of electric charge is the fact that it is mobile; it can be transferred from one place to another it can be converted to another form of energy  Basic Concepts Charge and Current CIRCUITS 1 Current (I) When a conducting wire (consisting of several atoms) is connected to a battery (a source of electromagnetic force), the (negative) charges are compelled to move. Flow of charges creates This motion of charges create current electriccurrent Electric current. is known by its magnitude and direction and is measured by unit amperes (A). The magnitude tells us the rate of flow of electric charge past a given point. The direction is from “the point of higher potential to the point of lower potential” for a given circuit element and by convention, this means opposite to the direction of flow of negative charges.  Basic Concepts Charge and Current CIRCUITS 1 Common Types of Current DIRECT CURRENT (DC) ALTERNATING o is a current that CURRENT (AC) remains constant with o is a current that varies time sinusoidally with time (time-varying current)  Basic Concepts Charge and Current CIRCUITS 1 Mathematical Relationship Between Charge and Current Varying Quantities Constant Quantities Q I= A t Q=It C  Basic Concepts Example 1.1 CIRCUITS 1 In an element, find the current at t = 1.0 s. q element 𝑞(𝑚𝐶) Solution: 10 mC 𝒅𝒒 𝒎𝑪 𝒊= =𝟐𝟎 𝒆 − 𝟐 𝒕 =𝟐𝟎 𝒆− 𝟐 𝒕 𝒎𝑨 , 𝒅𝒕 𝒔 − 2𝑡 𝑞=( 10 − 10 𝑒 ) − 𝟐 (𝟏 ) 𝒊 ( 𝟏. 𝟎 ) =𝟐𝟎 𝒆 =𝟐. 𝟕𝟎𝟕 𝒎𝑨 𝑡 → ∞ ,𝑞 → 10 𝑚𝐶 , 𝑖 → 0 1.0s 𝑡(s)  Basic Concepts Example 1.2 CIRCUITS 1 The charge flowing in a wire is plotted below. Sketch the corresponding current.  Basic Concepts Example 1.2 CIRCUITS 1 Solution i(A) 25 -25  Basic Concepts Example 1.3 CIRCUITS 1 The current through an element is shown below. Determine the total charge that passed through the element at (a) t = 1 s, (b) t = 3 s, and t = 5 s. Assume that no charge has passed thru the element before t = 0 s. q i element  Basic Concepts Example 1.3 CIRCUITS 1 Solution 40 q(C) q 27.5 30 17.5 20 i 10 element  Basic Concepts Resistance CIRCUITS 1 Is a circuit element that opposes flow of current. Analogous to friction (resistance) that opposes motion or movement (current flow). Resistors (that has resistance) are energy absorbers. They turn electrical energy directly into heat energy. Resistances are measured by the unit ohms (Ω). Carbon Resistors Symbol  Basic Concepts Voltage CIRCUITS 1 Voltage Voltage is a source of energy that cause charges to flow thereby creating current. Analogous to a physical force applied to an object that makes the latter move. Voltage (also called electromotive force or emf, or potential difference) is known by its magnitude and polarity. It is measured by the derived unit For a resistor, the magnitude of the voltage is volt (V) which means Joules/coulomb (J/C). i determined by the amount of current through it. Its polarity is determined by the actual direction of 𝑅 the current through it. The terminal where the actual Voltagecurrent can beenters is the classified as positive a voltageterminal source and the otherprovider, (energy terminalex. is then the negative battery) terminal. or a voltage drop (energy absorber, ex. voltage across a resistor).  Basic Concepts Voltage CIRCUITS 1 Voltage When voltage is applied across a length of wire, an electric field is created inside the wire running from the positive terminal of the source and back to its negative terminal. This field forces the electrons (which carry charges) on the atoms of the wire To to move move in the charged direction particles likeshown below thereby creating current i in the electrons opposite work requires direction. or energy. This energy is wire i provided by the voltage sources. If one joule of work is required from a - - voltage source to move one coulomb of Voltage - charge, that means that the source must have a magnitude of one volt. - - Voltage is the energy required to move a unit charge through an element, measured in volts (V). (Alexander & Sadiku, 2011) (electric field)  Basic Concepts Voltage CIRCUITS 1 Mathematical Relationship 𝑑𝑤 W 𝑣= V= V 𝑑𝑞 Q where: w, W = energy in joules (J) q, Q = charge in coulombs (C)  Basic Concepts Power and Energy CIRCUITS 1 Power As applied to circuit elements, is the rate at which I electrical energy is absorb or released by the element. The unit of power is Joules/sec (J/s) or watts (W). V element Every circuit element either absorbs or releases 𝑃=𝑉𝐼 power. Circuit elements that only absorb power, are called passive elements. Examples are resistors, capacitors, and inductors. I Circuit elements that can absorb or release power are 𝑃=𝑉𝐼 called active elements. Example is a voltage source V R like battery. In DC circuits, the power absorbed or released by an 2 𝑉 element is the product of the voltage across an ¿ element and the current through it 𝑅  Basic Concepts Power and Energy CIRCUITS 1 Power Power is said to be positive with respect to a given element if energy is absorbed by that element (current enters its positive terminal), otherwise, it is negative (current leaves the positive terminal). I I V element 𝑃=+ 𝑉𝐼 V element 𝑃=−𝑉𝐼 (negative power since I leaves the positive terminal) (positive power since I enters the positive terminal)  Basic Concepts Power and Energy CIRCUITS 1 Energy (W) Refers to the actual energy absorbed or released by an element over a specific period of time. If power P for the element is constant, then energy over a period of time from t = t0 to t = t1 is, 𝑊 = 𝑃 Δ 𝑡 = 𝑃 ( 𝑡 1 − 𝑡 0 ) =𝑉𝐼 ( 𝑡 1 − 𝑡 0 ) where; Common unit of energy is the watt-hr (W-Hr) or watt-sec (W-sec).  Basic Concepts Ohm’s Law CIRCUITS 1 The relationship between voltage, current, and resistance is illustrated by Ohm’s Law. I V R 𝑉 =𝐼𝑅 According to this law, the magnitude of the current I through a resistance R is proportional to the voltage V across that resistance. The direction of the current is such that it flows from the resistance positive terminal to its negative terminal.  Basic Concepts Ohm’s Law CIRCUITS 1 In the case of Fig. 1, since R is directly connected (via wires) to the source voltage E, its polarity (the location of positive and negative terminals) will inherit the polarity of the source. Similarly, the magnitude of the voltage across R will inherit E since it is directly connected. I I 𝑉 =𝐸 V 𝑽 𝑬 E R 𝑰= = 𝑹 𝑹 Fig. 1  Basic Concepts Ohm’s Law CIRCUITS 1 In the case of Fig. 2, since R is NOT anymore directly connected to the source voltage E, the previous equations won’t apply. I I 𝑅1 𝑽 𝑬 𝑰= ≠ E 𝑹 𝑹 V 𝑅 Fig. 2  Basic Concepts Example 1.4 CIRCUITS 1 In the circuit shown below, find the voltage across the and the power it absorbs. Also, find the energy dissipated in watt-hr for 1 hr. I I 𝑅1 =30 Ω 𝐸=50𝑉 𝑅2 =20 Ω Fig. 3  Basic Concepts Example 1.4 CIRCUITS 1 Solution I The two resistors are connected in I series (Fig. 4a), therefore they can 𝑅1 =30 Ω be added to form a single 50 Ω resistor (Fig. 4b), that is directly 𝐸=50𝑉 connected to the 50voltage source. 𝐼= =1 𝐴 𝑅2 =20 Ω 50 Fig. 4a The same current I passes through the resistors, therefore, I I 𝑉 2= 𝐼 𝑅2= ( 1 ) ( 20 )=20 𝑉 𝑃 2=𝑉 2 𝐼 =( 20 ) ( 1 ) =20 𝑊 𝐸=50𝑉 50 Ω W-hr Fig. 4b  Basic Concepts Circuit Elements CIRCUITS 1 Active Elements: capable of Passive Elements: absorb generating/supplying energy energy Circular-shaped sources are called Resistor dissipates energy independent sources, while diamond- while inductor and capacitor shaped sources are dependent sources. stores energy. Independent sources produce their own energy (ex. Battery) while dependent sources derive their energy from independent sources.  Basic Concepts Circuit Elements CIRCUITS 1 Linear and Non-Linear Elements Linear elements satisfies the homogeneity and additivity property of elements. Homogeneity requires that if the input to an element is multiplied by a constant, then its the output is multiplied by the same constant. i ki + + 𝒆 _ 𝑹 𝒌𝒆 _ 𝑹  Basic Concepts Circuit Elements CIRCUITS 1 Linear and Non-Linear Elements Additivity requires that the response of an element to a sum of inputs is the sum of the responses to each input applied separately. 𝒊𝟏 𝒊𝟐 𝒊𝟏 +𝒊 𝟐 𝒆𝟏 + _ 𝒆𝟏 + 𝒆𝟐 + _ 𝑹 _ 𝑹 𝑹 𝒆𝟐 + _  Basic Concepts Circuit Elements CIRCUITS 1 Linear and Non-Linear Elements Resistor: a good example of a linear element  Basic Concepts Circuit Elements CIRCUITS 1 Linear and Non-Linear Elements Diode: a good example of a non-linear element  Basic Concepts Circuit Elements CIRCUITS 1 Switches Used in circuits to connect and disconnect elements and circuits. Have two distinct states, open and closed. Fig. 5a Fig. 5b Ideally, acts like a; Short circuit when it is closed. SPST (Single-pole, single-throw) Open circuit when it is open switch The schematic symbol of a switch closing at time t = 0 is shown in Fig. 5a, while a switch opening at time t = 0 is shown in Fig. 5b. Basic Concepts CIRCUITS 1 Thank You