Integration Time-line Derivations and Problems Equivalent Capacitance: Capacitors in Series Capacitors in Parallel Voltage across capacitors Current flowing through capacitor Fundamental Forces of Nature Introduction to Magnetic Fields

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Session 15D: Focus
 Integration Time-line
 Derivations and Problems Equivalent Capacitance:
◦ Capacitors in Series
◦ Capacitors in Parallel
 Voltage across capacitors
 Current flowing through capacitor
 Fundamental Forces of Nature
 Introduction to Magnetic Fields

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Integration Time-line

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Integration Time-line (t0) Explained
 There is no year 0, after 1 BC, AD 1 starts. AD 1 is considered to be the
year of birth of Lord Jesus Christ (actually between 6 BC and 4 BC)
4
- ∞ +∞
Time line
t0
|
Initial time
Current time
|
Calendar Analogy – Gregorian Calendar

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Capacitors in Parallel

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Capacitors in Parallel
 Applying KCL we get the following relationship

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Capacitors in Series

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Capacitors in Series
 Applying KVL to the loop, we get the following:

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Capacitors in Series … contd.
 The initial voltage across the Cequ is the sum of the
initial voltages across all the capacitors in series
 Capacitors in series combine in the same manner
as resistors in parallel.

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Quiz 1: Find the Equivalent Capacitance
 Find the Ceq across a and b:
4 μF is in parallel with other two capacitors
So, 4 μF + 6 μF + 20 μF = 30 μF
30 μF is in series with 60 μF
Cequ = (30 μF * 60 μF) /(30 + 60) μF
Cequ = 20 μF
Cequ = 20 μF

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Quiz 2: Find the Equivalent Capacitance
 Find the Ceq: 40 μF

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Quiz 3: Find the Voltage across Each
Capacitors
 Find the voltages:
q = Ceq * v = 10 mF * 30 = 0.3 C
This is the charge on the series capacitors 20 mF and 30mF, since
The same current is flowing through them, so v1 and v2 can be computed as follows:
v1 = q/C1 = 0.3/20mF = 15 V
v2 = q/C2 = 0.3/30mF = 10 V
Using KVL, -30 + v1 + v2 + v3 = 0
v3 = 30 – 10 -15 = 5 V
mF is Milli Farad = 10-3 F
Because i= dq/dt

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Problem 1
Note: This is Example 7.1 on page 219, Figure 7.3 in the Ref 1 book (by Hayt)

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Fundamental Forces of Nature

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Fundamental Forces of Nature
(1. Strong Force)
 There are four of them:
1
Colour force
Does not follow inverse square law (distances are very small)
A force which can hold a nucleus together against the enormous forces
of repulsion of the protons is strong indeed.
Since the protons and neutrons which make up the nucleus are
themselves considered to be made up of quarks,
and the quarks are considered to be held together by the color force

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2. Electromagnetic Force (Electric)
 There are four of them:
2
Follows inverse square law
Electric and magnetic forces , same form as the Gravity force
The electromagnetic force holds atoms and molecules together.
Electric Forces

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2. Electromagnetic Force (Magnetic)
2
Magnetic Force
Right Hand Rule

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Magnetic Force on a Moving Charge
 The magnetic force on a
free moving charge is
perpendicular to both the
velocity of the charge and
the magnetic field with
direction given by
the right hand rule

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Fundamental Forces of Nature … contd.
 There are four of them:
3
4

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Session 15D: Summary
 Integration Time-line
 Derivations and Problems Equivalent
Capacitance:
◦ Capacitors in Series
◦ Capacitors in Parallel
 Voltage across capacitors
 Current flowing through capacitor
 Fundamental Forces of Nature
 Introduction to Magnetic Fields

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References
Ref 1 Ref 2