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PHY 102 (General Physics)
SESSION: 2019/ 20
Part I
TOPICS TO BE COVERED
1
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3
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5
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***Questions related to the course taught that could not be addressed in class should be sent as a mail to the
following e-mail phyquestionsaaua@gmail
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A solution in jpeg or pdf format will be sent back as a reply
within 2 – 3 days
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M
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A Source is an of electric generator that converts a form of energy into electrical energy
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This source is a generator with two oppositely charged terminals (positive
and negative) which are at different levels of potential and this results in a potential difference between the two
terminals which is capable of causing charge migration
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A battery is an example of an electrochemical
generator
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1: Symbol for EMF source and Battery
Electric current
The potential difference produced by a battery will cause charge migration from the region of high potential to the
region of low potential provided a migration path (a conductor) is provided
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It is given by I = dQ/dt
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Ohm’s Law
Ohm’s law gives the relationship between the Potential difference of a source and the current flowing in a
conductor connected across it
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In a circuit, resistors connected in series (end to end) add up to give one equivalent resistance while resistors
connected in parallel (tail to tail) add up to give an equivalent resistance equal to the sum of their inverses
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To analyze these types of
circuit, we employ the Kirchhoff’s laws
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Kirchhoff Current Law
This law states that the sum of all currents entering a junction is equal to the sum of the current leaving the junction
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e
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Consider the
junction below,
I4
I5

I1

I2
2

I3

Here, the current is given by
𝐼 + 𝐼 = 𝐼 + 𝐼 + 𝐼
2
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This implies that in a simple circuit network, EMF must be equal to the potential difference across the
resistance
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To analyze a circuit using the voltage law, the following steps can be adopted;
1
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Label the current in each branch
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Apply KCL to every junction in the circuit
4
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Pick a loop and chooses an arbitrary starting point for the direction to go in the loop
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Apply KVL to the loop under the following conditions
i
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If the direction of current flow from the source (The + ive terminal) is the same as the direction to
go, the EMF of the source is +E
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7
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Apply the loop principle for all loops
9
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If a current has a negative value, this implies that its direction is opposite the direction initially assigned to it
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Solution:
I1 = 1
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75, I3 = 0
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Certain
sources such as batteries and Photovoltaic cells can provide current flow only from fixed terminals (the positive
terminal) i
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the polarity of the source is never reversed and the direction of current flow is always in one direction
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Other sources in which the direction of current flow changes periodically (at regular intervals) are called
Alternating current (AC) sources
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Nonetheless, an AC sources
can be configured to produce Direct current through a process called rectification
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Here, we introduce the capacitor and the inductor and study their
behaviors under Alternating current
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The EMF of an AC source can be represented by
equations describing an oscillating particle
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The time dependence of the EMF is given by a periodic cosine function i
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𝑉

cos(𝜔𝑡)

The root mean square (rms) value of the AC source 𝑉
equal to that of a DC source with an EMF of 𝑉

is the voltage at which the source will dissipate a power

in a given resistor R is given by;

𝑉

=𝑉

/ √2

Simple resistive circuit
A resistor connected across an AC source from ohms law will have a current given by I = V/R

Fig 2
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The root mean square value of the current is given by 𝐼
=𝐼
/ √2
4

The power dissipated in the resistor is given by P = IV
𝑃= 𝑉
cos(𝜔𝑡) × 𝐼
cos(𝜔𝑡) = 𝑉
𝑐𝑜𝑠 (𝜔𝑡) / 𝑅
P=𝑉
/𝑅
The power dissipated in the resistor is always positive
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In DC circuits, charge flow from the
source through a capacitor only when it is charging up
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Fig 2
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The capacitor has a reactance given by XC
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e
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Its unit is in Ohms
I can then be written as 𝐼 = −𝑉
sin(𝜔𝑡) / 𝑋
The instantaneous power delivered to the capacitor is given by; 𝑃 = 𝐼𝑉 = −𝜔𝐶𝑉
The average power dissipated by the capacitor (an ideal) is zero
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Simple Inductive circuit
An ideal inductor is a simple coil of wire without a resistance
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In AC circuits, the current flow in the inductor is limited by self-inductance in which the application of
AC current across the inductor generates a back EMF that tends to oppose further increase in current
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3: A Simple inductive circuit
The EMF induced in an inductor connected across a source 𝑉 = 𝑉
cos(𝜔𝑡) is given by;
𝐿𝜕𝐼
𝐿𝜕𝐼
𝑉−
= 0; 𝑉 =
; 𝜕𝐼/𝜕𝑡 = 𝑉/𝐿
𝜕𝑡
𝜕𝑡
Where L is the inductance of the inductor
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The inductor has a reactance XL
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e
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Its unit is in Ohms
The instantaneous power delivered to the inductor is given by 𝑃 = 𝐼𝑉 = 𝑉
sin(𝜔𝑡) cos(𝜔𝑡) / 𝜔𝐿
The average power dissipated by the inductor (ideal) is zero
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The simplest representation
involves a single resistor, an inductor and a resistor connected in series with an AC source as shown in figure 2
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The total opposition to the flow of current is called the impedance (Z) of the circuit and it is made up in part by
the resistance, the capacitive reactance and the inductive reactance (not the sum)
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5
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4: A simple RLC Circuit

Figure 2
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Phasor diagram of an RLC circuit
It can be seen that same current I0 flow in all the circuit elements and it agrees with the notion of VR in phase with
current and voltage leading and lagging current in VC and VL
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6: Resolved Phasor diagram of an RLC circuit
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The resultant voltage Vo is then given by the vectoral sum of both voltages and it has a magnitude given by
𝑉 =

𝑉

+ (𝑉 − 𝑉 )

Each value of V above represents the peak values of the voltages
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Therefore,
𝑃=𝐼
𝑉 cos ∅
Where cos ∅ is the power factor and it is given by cos ∅ = 𝑅/𝑍
In a circuit without resistance P = 0
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Find the current flowing in the circuit
2
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Solution
First compute the values of the impedance from the values given
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Irms = 1
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2V, VL(rms) = 118V, VC(rms) = 33
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In an RLC circuit, the vibrating force is produced by the AC source and the
natural or resonant frequency (𝑓 ) of the circuit is the point at which Irms is maximum
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e Z = R
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2𝜋𝑓 𝐿 – 1/2𝜋𝑓 𝐶 = 0
𝑓 = 1/2𝜋√𝐿𝐶
For situations where R is very small, the total energy of the system oscillates at the resonant frequency between
the capacitor and inductor
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These types of circuits are called LC circuits, oscillators and the oscillation is termed
electromagnetic oscillation
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Exercise 2:
Find the resonant frequency of the circuit in example 2 above
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Although they have bands completely filled with electrons, the energy gap between the last full band and the next
empty band is much smaller than that of an insulator
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Examples of semiconductors are Silicon, Germanium and Gallium
Arsenide
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The process of adding these impurities is called doping and the type of semiconductor obtained is
determined by the type of impurity used in the doping process
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Elemental silicon has four outer electrons
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The addition of
this few extra atoms greatly increases the conductivity of the semiconductor as the electrons acts as majority charge
carriers
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The three outer electrons in the boron atom bounds with the silicon atom but leaves
an empty hole behind
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This mobile hole acts as a charge carrier
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In this type of
semiconductors, the holes are the majority charge carriers
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A n-type semiconductor and a p-type semiconductor can be joined together to form a P-N junction
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At the junction, some free
electrons diffuse through the junction and combine with the holes
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The junction is called the depletion layer because it
is devoid of charge carriers (i
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all the holes are filled with electrons)
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1: A forward biased diode
When an EMF source such as a battery is connected across the diode with the +ive terminal to the p-type
semiconductor (as shown above), the EMF opposes the intrinsic potential difference that halted movement of
charge carriers
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6V and if the EMF source is greater than this,
current floes in the from the P–N channel and the diode is said to be forward biased
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A diode is a non ohmic conductor as the graph
of output voltage vs output current is not a straight line graph
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This is done by allowing current to flow only in the positive half cycle and blocking
current flow during the negative half cycle
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Solar Cells
These are heavily doped PN junctions that are capable of generating a potential by creating electron hole pairs
after the absorption of photons of sunlight
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6 V and by connecting a
lot of them in series, higher voltage outputs can be achieved
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Light Emitting Diodes (LEDs)
LEDS are the reverse of Photovoltaic cells i
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they emit photons when a potential difference is applied between
them
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Si diodes do not fare well in these applications and mostly Gallium Arsenide (GaAn)
or Gallium Arsenide Phosphorous (GaAsP) compound type semiconductors are used
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Other uses of the P-N diode are Laser diode, Organic LEDs (OLEDs), and electronic circuit protection
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They
are majorly of two types
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Each can be subdivided into NPN
or PNP and N-Channel or P-Channel based on the materials used in making them
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10

Fig 3
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This makes the package very
small while housing a lot of circuits
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Some integrated circuits
contain several billion transistors or MOSFETs and they can thus perform a lot of different operations
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The microprocessor employed in the development of Computers is a key example
and the latest variants (core i7) contains about 1
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2cm
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