Transcript ppt
0 EE 1270: Introduction to Electric Circuits Lecture 15: Inductor & Capacitor Chapter 6 Inductance, Capacitance, and Mutual Inductance Sections 6.1-6.3 EE 1270 Introduction to Electric Circuits Suketu Naik EE 1270: Introduction to Electric Circuits 1 Inductor EE 1270 Introduction to Electric Circuits Suketu Naik 2 Inductor An inductor consists of a coil of conducting wire (e.g. copper) An inductor is a passive element designed to store energy in its magnetic field Inductor exhibits opposition to the change of current flowing through it: this is known as Inductance (unit=henrys or H). EE 1270 Introduction to Electric Circuits Suketu Naik 3 Applications of Inductor Power Transmission Lines and Utility Substation Power Supply Tranceiver PCB EE 1270 Introduction to Electric Circuits Memory Control PCB Suketu Naik Inductor Basics Circuit Symbol 4 Practical Inductor An inductor opposes an abrupt change in the current through it (the voltage across an inductor can change abruptly) The ideal inductor does not dissipate energy. It takes power from the circuit when storing energy and delivers power to the circuit when returning previously stored energy A practical, non-ideal inductor has small resistive component, called winding resistance: it dissipates energy. A practical, non-ideal inductor also has small winding capacitance due to the capacitive coupling between the conducting coils. Parasitic resistor and inductor are ignored at low frequencies EE 1270 Introduction to Electric Circuits Suketu Naik 5 Inductor di vL dt Where L=inductance [H], i=current [A], v=voltage [V], t=time [s] N 2 A L l where N=the number of turns, l=length, A=cross-sectional area, μ=permeability of the core. Any conductor of electric current has inductive properties and may be regarded as an inductor In order to enhance the inductive effect, a practical inductor is usually formed into a cylindrical coil with many turns of conducting wire EE 1270 Introduction to Electric Circuits Suketu Naik Example 6.1: Inductor Current-Voltage Characteristics 6 Q: Find and sketch the voltage across the inductor A: Method 1: Solve the inductor equation, Method 2: Simulate EE 1270 Introduction to Electric Circuits Suketu Naik 7 Current in terms of Voltage Across the Inductor Example 6.2 Q: Find and sketch the inductor current A: Method 1: Solve the inductor equation, Method 2: Simulate EE 1270 Introduction to Electric Circuits Suketu Naik AP6.1a, c, g : Voltage, Current, Power, Energy in Inductor EE 1270 Introduction to Electric Circuits 8 Suketu Naik Combining Inductors 9 What is Leq for series and parallel combinations? EE 1270 Introduction to Electric Circuits Suketu Naik AP6.4a-c*: Current, Voltage in Parallel Inductors 10 * in class excercise EE 1270 Introduction to Electric Circuits Suketu Naik EE 1270: Introduction to Electric Circuits 11 Capacitor EE 1270 Introduction to Electric Circuits Suketu Naik 12 Applications of Capacitors Store Charge in Circuits Welding Machine Power Filter Graphene based Flexible Supercapacitor Battery EE 1270 Introduction to Electric Circuits Suketu Naik Applications of Capacitors Power Factor Correction in Transmission Line (Ref) 13 AC Adapters EE 1270 Introduction to Electric Circuits Suketu Naik Applications of Capacitors Tablets and Smart Phones 14 Capacitor Proximity Switch in Elevators EE 1270 Introduction to Electric Circuits Suketu Naik Capacitor Basics Circuit Symbol 15 Practical Capacitor A Capacitor opposes an abrupt change in the voltage across it (the current across a capacitor can change abruptly) The ideal capacitor takes power from the ciruit and stores the energy: we denote this operation as, "capacitor charges up..." A practical, nonideal capacitor has a small resistive component, called Equivalent Series Resistance (ESR): it discharges the cap. A practical, noideal inductor also has small Equivlent Series Inductance (ESL) due to the capacitive coupling between the capacitor leads or PCB traces or pads We ignore ESR and ESL at low frequencies EE 1270 Introduction to Electric Circuits Suketu Naik 16 Capacitor Ceramic Capacitor Electrolytic Capacitor Surface Mount Capacitor A capacitor consists of two conducting layers separated by dielectic material A capacitor is a passive element designed to store energy in its electric field Capacitance is the ratio of the charge on one plate of a capacitor to the voltage difference between the two plates (unit=farads or F) EE 1270 Introduction to Electric Circuits Suketu Naik 17 Capacitor A C ; d q CV dq dV iC dt dt Where, C=capacitance [F], ε=dielectric constant [N/A2], A=overlapping area [m2], d=gap [m], q=charge accumulated on the plates, i=current across the capacitor Higher the dielectric* constant, higher the capacitance Smaller the gap, higher the capaictance Larger the area, higher the capacitance * More info on dielectrics can be found at: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/dielec.html EE 1270 Introduction to Electric Circuits Suketu Naik 18 AP 6.2 Voltage, Current, Power and Energy in a Capacitor v 0....t 0 v 40e 15000t sin( 30000t )...t 0 1) Given the voltage find the capacitor current at t=0 2) Find the power delivered to the capacitor at t=π/80 ms 3) Find the energy stored in the capacitor at t=π/80 ms EE 1270 Introduction to Electric Circuits Suketu Naik Series and Parallel Combination of Capacitors EE 1270 Introduction to Electric Circuits 19 Suketu Naik P6.27: Series and Parallel Combination of Capacitors EE 1270 Introduction to Electric Circuits 20 Suketu Naik Always Remember!! 21 An inductor will act as a short at DC (low frequency) and open at AC (high frequency) low frequency high frequency A capacitor will act as an open at DC (low frequency) and short at AC (high frequency) low frequency high frequency EE 1270 Introduction to Electric Circuits Suketu Naik