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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
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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
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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
vL
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
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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
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Suketu Naik
Combining Inductors
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What is Leq for series and parallel combinations?
EE 1270 Introduction to Electric Circuits
Suketu Naik
AP6.4a-c*: Current, Voltage in Parallel Inductors
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* 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)
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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
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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
iC
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
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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
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P6.27: Series and Parallel Combination of Capacitors
EE 1270 Introduction to Electric Circuits
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Suketu Naik
Always Remember!!
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 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