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 Inductor

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).

Applications of Inductor Power Transmission Lines and Utility Substation Power Supply Tranceiver PCB Memory Control PCB

Parasitic resistor and inductor are ignored at low frequencies Inductor Basics Circuit Symbol 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

Inductor 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. 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

Example 6.1: Inductor Current-Voltage Characteristics Q: Find and sketch the voltage across the inductor A: Method 1: Solve the inductor equation, Method 2: Simulate

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

AP6.1a, c, g : Voltage, Current, Power, Energy in Inductor

Combining Inductors What is Leq for series and parallel combinations?

AP6.4a-c*: Current, Voltage in Parallel Inductors * in class excercise

EE 1270: Introduction to Electric Circuits Capacitor

Applications of Capacitors Store Charge in Circuits Welding Machine Power Filter Graphene based Flexible Supercapacitor Battery

Applications of Capacitors Power Factor Correction in Transmission Line (Ref) AC Adapters

Applications of Capacitors Tablets and Smart Phones Capacitor Proximity Switch in Elevators

We ignore ESR and ESL at low frequencies Capacitor Basics Circuit Symbol 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

Capacitor Ceramic Capacitor Electrolytic Capacitor Surface Mount 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)

Capacitor Higher the dielectric* constant, higher the capacitance 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

AP 6.2 Voltage, Current, Power and Energy in a Capacitor 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

Series and Parallel Combination of Capacitors

P6.27: Series and Parallel Combination of Capacitors

Always Remember!! An inductor will act as a short at DC (low frequency) and open at AC (high frequency) A capacitor will act as an open at DC (low frequency) and short at AC (high frequency) low frequency high frequency low frequency high frequency