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ECE 1270 Introduction to Electric Circuits Suketu Naik
0ECE 1270: Introduction to Electric Circuits
Lecture 15:
Inductor & Capacitor
Chapter 6
Inductance, Capacitance, and
Mutual Inductance
Sections 6.1-6.3
ECE 1270 Introduction to Electric Circuits Suketu Naik
1EE 1270: Introduction to Electric Circuits
Inductor
ECE 1270 Introduction to Electric Circuits Suketu Naik
2Inductor
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).
ECE 1270 Introduction to Electric Circuits Suketu Naik
3Applications of Inductor
Power Transmission Lines and Utility Substation
Power
SupplyTranceiver PCB Memory Control PCB
ECE 1270 Introduction to Electric Circuits Suketu Naik
4Inductor Basics
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
Circuit Symbol Practical Inductor
ECE 1270 Introduction to Electric Circuits Suketu Naik
5Inductor
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
dt
diLv
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.
l
ANL
2
ECE 1270 Introduction to Electric Circuits Suketu Naik
6Example 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
ECE 1270 Introduction to Electric Circuits Suketu Naik
7Current in terms of Voltage Across the Inductor
Q: Find and sketch the inductor current
A: Method 1: Solve the inductor equation, Method 2: Simulate
Example 6.2 (Omit)
ECE 1270 Introduction to Electric Circuits Suketu Naik
8AP6.1a, c, g : Voltage, Current, Power, Energy in Inductor
ECE 1270 Introduction to Electric Circuits Suketu Naik
9Combining Inductors
What is Leq for series and parallel combinations?
ECE 1270 Introduction to Electric Circuits Suketu Naik
10P6.22b: Series and Parallel Combination of Inductors
ECE 1270 Introduction to Electric Circuits Suketu Naik
11EE 1270: Introduction to Electric Circuits
Capacitor
ECE 1270 Introduction to Electric Circuits Suketu Naik
12Applications of CapacitorsStore Charge in Circuits
Welding Machine Power FilterGraphene based Flexible Supercapacitor
Battery
ECE 1270 Introduction to Electric Circuits Suketu Naik
13Applications of CapacitorsPower Factor Correction in
Transmission Line (Ref) AC Adapters
ECE 1270 Introduction to Electric Circuits Suketu Naik
14Applications of CapacitorsTablets and Smart Phones Capacitor Proximity Switch
in Elevators
ECE 1270 Introduction to Electric Circuits Suketu Naik
15Capacitor Basics
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
Circuit Symbol Practical Capacitor
ECE 1270 Introduction to Electric Circuits Suketu Naik
16Capacitor
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)
Ceramic Capacitor Surface Mount
Capacitor
Electrolytic Capacitor
ECE 1270 Introduction to Electric Circuits Suketu Naik
17Capacitor
Higher the dielectric* constant, higher the capacitance
Smaller the gap, higher the capaictance
Larger the area, higher the capacitance
;d
AC
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
dt
dVCi
dt
dq
CVq
* 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
18AP 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
0)...30000sin(40
0....0
15000
ttev
tv
t
ECE 1270 Introduction to Electric Circuits Suketu Naik
19Combining Capacitors
What is Ceq for series and parallel combinations?
ECE 1270 Introduction to Electric Circuits Suketu Naik
20P6.27: Series and Parallel Combination of Capacitors
Q: How do you combine two parallel caps with different
voltages?
ECE 1270 Introduction to Electric Circuits Suketu Naik
21Always 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
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