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CAPACITORS
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A BRIEF DISCUSSION ABOUT ELECTRIC FIELD
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Basically an electric field is defined by the region where an electric
charge will experience a force.
 It exists around any charged body.
The field can be represented by a set of lines known as electric flux
lines.
 This lines are drawn to represent the strength of the electric field
around the charged body; greater the number of lines, stronger
the electric field.
Consider this diagram:
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A BRIEF DISCUSSION ABOUT ELECTRIC FIELD
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is used to represent the electric flux.
D (flux density) is used to represent the flux per unit area.
So,
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Now, If Q increases, flux lines also increases.
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So,
Electric Field Strength, , at a point is defined as the force acting on
an unit positive charge at that point, i.e
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A BRIEF DISCUSSION ABOUT ELECTRIC FIELD
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The force on a unit positive charge, Q2=1 at any point C, by another
positive charge, Q1, at a distance r is:
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Therefore, Electric Field Strength,
point C can be defined as:
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Therefore, Electric flux is:
, at the
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INTRODUCTION ABOUT CAPACITANCE
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Unlike resistors, which dissipate energy, capacitors do not dissipate
but store energy, which can be retrieved at a later time. For this
reason, capacitors are called storage elements.
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CAPACITORS
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A capacitor is a passive element.
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It is designed to store energy in its electric field
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It is used in electronics, communications, computers,
and power systems.
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CAPACITANCE, C
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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.
So capacitor is storing the charge.
The amount of charge stored is proportional to the
voltage applied
Let’s assume:
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Amount of charge stored = q
Voltage applied = v
q is proportional to v.
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Then we can write:
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Or,
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where C is a proportionality constant, known as
Capacitance
Unit of capacitance is farad (F).
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C = q/v
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CAPACITANCE, C
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In fact, Capacitance does not depend on q or V.
It depends on:
 the surface area of the plate, the larger the area, the greater
the capacitance.
 distance between the plates, the smaller the distance, the
greater the capacitance.
 Permittivity of the material, the higher the permittivity, the
greater the capacitance.
Permittivity is a measure of how easily the dielectric will
“permit” the establishment of flux lines within the
dielectric.
The greater its value, the greater the amount of charge
deposited on the plates, and, consequently, the greater
the flux density for a fixed area.
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CAPACITANCE, C
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TYPES OF CAPACITORS
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Fixed capacitor
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Variable capacitor
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CURRENT-VOLTAGE RELATIONSHIP OF A CAPACITOR
o Also, voltage can be written
as
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Taking derivative of q w.r.t time
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And
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So, the Current through any
capacitor is directly proportional to
the rate of change of voltage
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If there is NO change of voltage
across a capacitor, there will be NO
current flow
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ENERGY STORED IN A CAPACITOR
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The instantaneous power delivered to the capacitor is
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The energy stored in the capacitor is thus,
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Or,
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FEATURES OF A CAPACITOR
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When we apply dc voltage, current through the
capacitor is zero, i.e, capacitor is an open circuit
to dc.
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The voltage on a capacitor cannot change
abruptly.
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The ideal capacitor does not dissipate energy.
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A real, non ideal capacitor has a parallel-model
leakage resistance, as shown in Fig. 6.8.
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This tells us that a current will flow through this
resistor when the external voltage is removed and
the capacitor will discharge.
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EXAMPLE
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EXAMPLE
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EXAMPLE
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EXAMPLE
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EXAMPLE
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EXAMPLE
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SERIES AND PARALLEL CAPACITORS
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SERIES AND PARALLEL CAPACITORS
 For two capacitors is series,
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EXAMPLE
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EXAMPLE
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TRANSIENTS IN CAPACITIVE NETWORK - CHARGING
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Consider this circuit given below:
When switched to 1, the capacitor starts to charge, and there is a current flow
As the capacitor gets charged, the current decays, and becomes zero when it is
fully charged
The current IC of a capacitive network is essentially zero after five
time constants of the charging phase have passed in a dc network.
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TRANSIENTS IN CAPACITIVE NETWORK - CHARGING
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Current through the capacitor is,
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Voltage across the capacitor is,
Voltage across the resistor is,
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EXAMPLE
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TRANSIENTS IN CAPACITIVE NETWORK - DISCHARGING
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Discharging voltage
Discharging Current
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Problem Ex 10.8:
Solution to Ex 10.8:
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INITIAL VALUE S:
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Eq. (10.23
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THEVENIN EQUIVALENT: RTHC
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Ref.
- Fundamentals of Electric Circuits (3rd Edition)
by Charles K. Alexander and Mathew N.O.Sadiku
- Introcuctory Circuit Analysis (10th Edition)
by Boylestad
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