0. EE 1270: Introduction to Electric Circuits
Lecture 15:
Inductor & Capacitor
Chapter 6
Inductance, Capacitance, and Mutual Inductance
Sections

1. EE 1270: Introduction to Electric Circuits
Inductor

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).

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

4. 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

5. 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

6. 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

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

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

9. Combining Inductors
What is Leq for series and parallel combinations?

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

11. EE 1270: Introduction to Electric Circuits
Capacitor

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

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

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

15. 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

16. 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)

17. 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:

18. 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

19. Series and Parallel Combination of Capacitors

20. P6.27: Series and Parallel Combination of Capacitors

21. 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