Electrical Circuits (I) – 0903211
EE Department
The University of Jordan
Instructor: Dr. Yazid Khattabi
Dr. Yazid Khattabi. Electric Circuits (1)
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Chapter 6: Capacitors and Inductors
Lecture#1
Reference:
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Overview
❑ Two new linear (passive) circuit elements will be
introduced:
✓ The capacitor.
✓ The inductor.
❑ They do not dissipate energy, but instead, they store
energy.
❑ Called storage elements.
❑ Practical circuit application are composed of resistor,
capacitors and inductors.
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Capacitors
❑ It is a passive element.
❑ It stores energy in its electric field.
❑ It consists of two conducting plates
separated by an insulator (or dielectric).
❑ The plates are typically aluminum foil.
❑ The dielectric is often air, ceramic, paper,
plastic, or mica.
❑ Each capacitor has a capacitance 𝐂
measured in Farads (F).
❑ The symbol:
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Capacitors
❑ 1 F = 1 Coulomb/Volt.
❑ Most capacitors are rated in pF and μF.
❑ Capacitance is determined by the
geometery of the capacitor:
✓ Proportional to the area of the plates (A).
✓ Inversely proportional to the space
between them (d).
A
C=
d
where is the permittivity of the dielectric.
:
• Note more details will be covered in EM
courses.
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Capacitors
❑ A capacitor stores charges (energy) on 𝑖
its plates! How??
▪ When a voltage source v is connected to
the capacitor, the source deposits a
positive charge q on one plate and a
negative charge –q on the other (these
charges will be equal in magnitude).
▪ The amount of stored charge is ▪In general 𝑞 = 𝑞(𝑡) and
proportional to the voltage: 𝑣 = 𝑣 𝑡 , and 𝑖 = 𝑖 𝑡 .
q = Cv ▪Note: if 𝑣 = 𝑉 (DC), then
𝑞 = 𝑄 and 𝑖 = 0,i.e., the
capacitor = O.C (see later!)
Note: The value of 𝐶 does
not depend on 𝑣 or 𝑞.
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Capacitors
❑ For capacitor Types, shapes, and
applications see the textbook!
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Capacitor Current-Voltage Relationship
▪ By taking the first derivative of
𝑞 𝑡 = 𝐶𝑣(𝑡)
with respect to time 𝑡, we can have:
𝑖
dv
i=C
dt
▪ Note: this assumes the
passive sign
convention.
Note: if 𝑣𝑖 > 0 the capacitor is charging.
if 𝑣𝑖 < 0 the capacitor is discharging
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Capacitor Current-Voltage Relationship
𝑑𝑣
▪ If 𝑣 = 𝑉 (DC), then 𝑖 = 𝐶 = 0.
𝑑𝑡
▪ Also 𝑞 = 𝑄 (constant stored charge).
𝑖
▪ This means that with DC voltage applied to
the terminals no current will flow, i.e., the
capacitor is open circuit (o.c).
▪ However, the voltage on the capacitor’s
plates can’t change instantaneously.
▪ The capacitor’s voltage is continuous
function of 𝑡
▪ An abrupt (sudden) change in voltage
would require an infinite current (see the
equation)!
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Capacitor Current-Voltage Relationship
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Capacitor Current-Voltage Relationship
▪ The cap’s voltage can be obtained from the current by:
where 𝑣(𝑡𝑜 ) is the cap’s voltage at the initial time 𝑡𝑜 . It can be obtained
𝑞(𝑡 )
from the initial stored charge by 𝑣 𝑡𝑜 = 𝑜 .
𝐶
▪ Proof:
▪ Note: this shows the capacitor has a memory, which is often
exploited in circuits.
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Energy Stored in the Capacitor
▪ The energy stored in the capacitor is computed by:
Or
▪ Proof:
𝑑𝑤 1 𝑑𝑣
▪ Check: 𝑝 = = 𝐶 × 2𝑣 = 𝑣𝑖
𝑑𝑡 2 𝑑𝑡
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Thank You
Dr. Yazid Khattabi. Electrical Circuits (I). The University of Jordan
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