ECE 1270 Introduction to Electric Circuits 0 Lecture

ECE 1270: Introduction to Electric Circuits 0 Lecture 15: Inductor & Capacitor Chapter 6 Inductance, Capacitance, and Mutual Inductance Sections 6. 1 -6. 3 ECE 1270 Introduction to Electric Circuits Suketu Naik

EE 1270: Introduction to Electric Circuits 1 Inductor ECE 1270 Introduction to Electric Circuits Suketu Naik

Inductor 2 p An inductor consists of a coil of conducting wire (e. g. copper) p An inductor is a passive element designed to store energy in its magnetic field p Inductor exhibits opposition to the change of current flowing through it: this is known as Inductance (unit=henrys or H). ECE 1270 Introduction to Electric Circuits Suketu Naik

3 Applications of Inductor Power Transmission Lines and Utility Substation Power Supply Tranceiver PCB ECE 1270 Introduction to Electric Circuits Memory Control PCB Suketu Naik

Inductor Basics Circuit Symbol 4 Practical Inductor p An inductor opposes an abrupt change in the current through it (the voltage across an inductor can change abruptly) p 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 p A practical, non-ideal inductor has small resistive component, called winding resistance: it dissipates energy. p 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 ECE 1270 Introduction to Electric Circuits Suketu Naik

Inductor 5 Where L=inductance [H], i=current [A], v=voltage [V], t=time [s] where N=the number of turns, l=length, A=cross-sectional area, μ=permeability of the core. p Any conductor of electric current has inductive properties and may be regarded as an inductor p In order to enhance the inductive effect, a practical inductor is usually formed into a cylindrical coil with many turns of conducting wire ECE 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 ECE 1270 Introduction to Electric Circuits Suketu Naik

7 Current in terms of Voltage Across the Inductor Example 6. 2 (Omit) Q: Find and sketch the inductor current A: Method 1: Solve the inductor equation, Method 2: Simulate ECE 1270 Introduction to Electric Circuits Suketu Naik

AP 6. 1 a, c, g : Voltage, Current, Power, Energy in Inductor ECE 1270 Introduction to Electric Circuits 8 Suketu Naik

Combining Inductors 9 What is Leq for series and parallel combinations? ECE 1270 Introduction to Electric Circuits Suketu Naik

P 6. 22 b: Series and Parallel Combination of Inductors ECE 1270 Introduction to Electric Circuits 10 Suketu Naik

EE 1270: Introduction to Electric Circuits 11 Capacitor ECE 1270 Introduction to Electric Circuits Suketu Naik

Applications of Capacitors 12 Store Charge in Circuits Welding Machine Power Filter Graphene based Flexible Supercapacitor Battery ECE 1270 Introduction to Electric Circuits Suketu Naik

Applications of Capacitors Power Factor Correction in Transmission Line (Ref) 13 AC Adapters ECE 1270 Introduction to Electric Circuits Suketu Naik

Applications of Capacitors Tablets and Smart Phones 14 Capacitor Proximity Switch in Elevators ECE 1270 Introduction to Electric Circuits Suketu Naik

Capacitor Basics Circuit Symbol 15 Practical Capacitor p A Capacitor opposes an abrupt change in the voltage across it (the current across a capacitor can change abruptly) p The ideal capacitor takes power from the ciruit and stores the energy: we denote this operation as, "capacitor charges up. . . " p A practical, nonideal capacitor has a small resistive component, called Equivalent Series Resistance (ESR): it discharges the cap. p 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 ECE 1270 Introduction to Electric Circuits Suketu Naik

Capacitor Ceramic Capacitor Electrolytic Capacitor 16 Surface Mount Capacitor p A capacitor consists of two conducting layers separated by dielectic material p A capacitor is a passive element designed to store energy in its electric field p 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) ECE 1270 Introduction to Electric Circuits Suketu Naik

Capacitor 17 Where, C=capacitance [F], ε=dielectric constant [N/A 2], A=overlapping area [m 2], d=gap [m], q=charge accumulated on the plates, i=current across the capacitor p Higher the dielectric* constant, higher the capacitance p Smaller the gap, higher the capaictance p Larger the area, higher the capacitance * More info on dielectrics can be found at: http: //hyperphysics. phy-astr. gsu. edu/hbase/electric/dielec. html ECE 1270 Introduction to Electric Circuits Suketu Naik

AP 6. 2 Voltage, Current, Power and Energy in a Capacitor 18 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 ECE 1270 Introduction to Electric Circuits Suketu Naik

Combining Capacitors 19 What is Ceq for series and parallel combinations? ECE 1270 Introduction to Electric Circuits Suketu Naik

P 6. 27: Series and Parallel Combination of Capacitors 20 Q: How do you combine two parallel caps with different voltages? ECE 1270 Introduction to Electric Circuits Suketu Naik

Always Remember!! 21 p An inductor will act as a short at DC (low frequency) and open at AC (high frequency) low frequency high frequency p A capacitor will act as an open at DC (low frequency) and short at AC (high frequency) low frequency high frequency ECE 1270 Introduction to Electric Circuits Suketu Naik