Electric Circuits PDF

Electric Circuits Circuit Elements D. Ahmed Tohamy Electronics and Communications Department Faculty of Engineering Sphinx University 1  Structure Voltage and Current Sources Elect...

Electric Circuits Circuit Elements D. Ahmed Tohamy Electronics and Communications Department Faculty of Engineering Sphinx University 1  Structure Voltage and Current Sources Electrical Resistance (Ohm's Law) Construction of a Circuit Model Kirchhoff’s Laws Electric Circuits 2  Circuit Elements When we speak of Circuit Elements, It is important to differentiate between the physical device itself and the mathemaical model which we will use to analyze its behavior in a circuit. We will use the expression circuit element to refer to the mathematical model. All the simple circuit elements that we will consider can be classified according to the relaionship of current through the element to the voltage across the element. Electric Circuits 3  Five ideal basic circuit elements Resistor Inductor Voltage source Current source Active elements Capacitor Passive elements Electric Circuits 4  Voltage and Current Sources Ideal voltage source: a circuit element that maintains a prescribed voltage across its terminals regardless of the current flowing in those terminals. Ideal Current source: a circuit element that maintains a prescribed current through its terminals regardless of the voltage across those terminals. Electric Circuits 6 Independent Sources An Independent source establishes a voltage or current in a circuit without relying on voltages or currents elsewhere in the circuit. The value of the voltage or current supplied is specified by the value of the independent source alone. Electric Circuits 7  Example #1 ✗ Which are valid? ✗ Electric Circuits 8  Dependent Sources A dependent source establishes a voltage or current whose value depends on the value of a voltage or current elsewhere in the circuit. You cannot specify the value of a dependent source unless you know the value of the voltage or current on which it depends. Four kind of controlled sources, – current‐controlled current source, CCCS; – voltage‐controlled current source, VCCS; – voltage‐controlled voltage source, VCVS; – current‐controlled voltage source, CCVS; Electric Circuits 9  The circuit symbols for (a)An ideal dependent voltage-controlled voltage source; (b)An ideal dependent current-controlled voltage source; (c) An ideal dependent voltage-controlled current source; (d)An ideal dependent current-controlled current source. Electric Circuits 10  Example #2 ✗ Which are valid? ✗ Electric Circuits 11  Example #3 For the circuit shown, – a) What value of vg is required in order for the interconnecion to be valid? – b) For this value of vg, find the power associated with the 8 A source. Electric Circuits 12  Solution for Example #3 For a), we have vg = ib/4 = −8/4 = −2(V) For b), we have p = 8vg = 8 × (−2) = −16(W) Electric Circuits 13  Electrical Resistance (Ohm's Law) Resistance is the capacity of materials to impede the flow of current or, more specifically, the flow of electric charge. The circuit element used to model this behavior is the resistor. The linear resistor is the simplest passive element. Its symbol and characterisic are as following: Electric Circuits 14  Ohm’s Law Left: in the direction of the voltage drop across the resistor Right: in the direction of the voltage rise across the resistor Electric Circuits 15  Other Forms of Ohm’s Law Current is in the direcion of the voltage drop across the resistor Current is in the direcion of the voltage rise across the resistor Conductance: the reciprocal of the resistance, which is symbolized by the letter G, and is measured in Siemens (S) Electric Circuits 16  Power in Different Forms Left: P = vi = (iR)i = i2R P = vi = v(v/R) = v2/R Right: P = −vi = −(−iR)i = i2R P = −vi = −v(−v/R) = v2/R The equaions for Left and right are identical and demonstrate clearly that, regardless of voltage polarity and current direction, the power at the terminals of a resistor is posiive. Therefore, a resistor absorbs power from the circuit. What’s the expression of power if we use conductance, rather than resistance? See example 2.3 (P.33) Electric Circuits 17  Example #4 Electric Circuits 18  Solution for Example #4 For a), we have R = vg/ig = 1 kV / 0.005 A = 200 kΩ p = vgig = 1000 V × 0.005 A = 5 W For b), we have vg＝p/ig = 3 W / 0.075 A = 40 V R = vg/ig = 40 V / 0.075 A = 533.3 Ω pabsorbed=pdelivered = 3 W For c), we have ig = (p/R)0.5= (0.48 W / 300 Ω)0.5 = 0.04 A = 40mA vg = (pR)0.5= (0.48 W × 300 Ω)0.5 = 12 V Electric Circuits 19  Construcion of a Circuit Model Flashlight An ideal switch offers no resistance to the current when it is in the ON state, but it offers infinite resistance to current when it is in the OFF state. Electric Circuits 20  In developing a circuit model, the electrical behavior of each physical component is of primary interest: a lamp, a coiled wire, and a metal case. Circuit models may need to account for undesired as well as desired electrical effects: light and heat. The arrangement of flashlight components Modeling requires approximaion. Electric Circuits 21  Example #5 The voltage and current are measured at the terminals of the device illustrated in (a), and the values of vt and it are tabulated in (b). Construct a circuit model of the device inside the box. Electric Circuits 22  Solution for Example #5 Plotting the voltage as a funcion of the In terms of Ohm's law, the current yields the graph shown in (a). The device inside the box behaves equaion of the line in this figure illustrates like a 4 Ω resistor. that the terminal voltage is directly proportional to the terminal current, vt=4it. Electric Circuits 23  Kirchhoff's Law A node is a point where two or more circuit elements meet. Circuit model for the flashlight Based on Ohm's law: Ohm's law may not be enough to provide a complete solution! Electric Circuits 24  Kirchhoff's current law (KCL): The algebraic sum of all the currents at any node in a circuit equals zero. Kirchhoff's voltage law (KVL): The algebraic sum of all the voltages around any closed path in a circuit equals zero. Reference direction is important! KCL: Assign a positive sign to a current leaving a node requires assigning a negative sign to a current entering a node, or vice versa. KVL: As we trace a closed path, assign a positive sign to a voltage rise requires assigning a negative sign to a voltage drop, or vice versa. Electric Circuits 25  Circuit model for the flashlight KCL KVL Electric Circuits 26  Example #6 Use Kirchhoff's current law (KCL) Electric Circuits 27  Solution for Example #6 Electric Circuits 28  Example #7 Electric Circuits 29  Solution for Example #7 Electric Circuits 30  Example #8 Use Ohm's law and Kirchhoff's laws to find the value of R in the circuit. vR iR i1 i2 v2 Kirchhoff’s laws: Ohm's law: vR + 120 – 200 = 0 R = vR / iR 120 – v2 = 0 24 i1 = 120 iR – i1 – i2 = 0 8 i2 = v2 R=4Ω Electric Circuits 31  Summary Ideal voltage/current sources Independent/dependent sources Resistor Ohm's law In series, closed path Kirchhoff's voltage/current law Electric Circuits 36