GENERAL PHYSICS 2
K to 12 Senior High School STEM Specialized Subject – General
Physics 2
I. Current, Resistance,
and Voltage
CURRENT
A difference in gravitational potential energy may cause mass to flow like
water flowing from an area of higher potential to an area of lower potential.
In the same manner, charges flow whenever there is a potential difference
(more commonly known as voltage) between the terminals of a source.
Electric current I, is the amount of charge passing through any point in a
conductor per unit time.
𝑄
I=
𝑡
where Q is the charge in coulombs and t is the time in seconds. The unit of
current is coulomb/second. This combination of units is called ampere (A).
Hence,
1A= 1C/s
The unit ampere is named after the French scientist and mathematician,
André Marie Ampère was considered the “Isaac Newton of electricity”. He
was the first to describe current as a continuous flow of electricity along a
wire. He founded the science of electrodynamics – the study of charges in
motion.
Example 1: A current of 1.5 amps (A) flows through a simple electrical
circuit. How many coulombs (Q) of charge flow through a point in 60
seconds?
Q=Ixt
Q = 1.5 A x 60 s
Q = 90 C
EXERCISE # 1
A steady current of 2.0 A flows in a wire for 16.0 s. (a) How many
coulombs of charge flow through the wire? (b) How many
electrons flow through the wire for the given time interval?
q = It = (2.0 A)(16.0 s) = 32 C
e =2.0 x 1020 electrons
Conventional Current vs Electron Current
In 1752, prior to electricity being identified with the electron, Benjamin Franklin
chose a convention regarding the direction of the current flow. Franklin
assumed that positive charge carriers flowed from positive to negative
terminals. We now know this is incorrect. In metals, the charge carrier is the
electron whose charge is negative by definition (note negative sign): (-1.6 x1019C).
The flow of electrons is termed electron current. Electrons flow from the
negative terminal to the positive. CONVENTIONAL CURRENT or simply
CURRENT, behaves as if positive charge carries cause current flow.
CONVENTIONAL CURRENT FLOWS from the positive terminal to the negative.
Perhaps the clearest way to think about this is to pretend as if movement of
positive charge carriers constituted current flow.
Conventional Current vs Electron Current
Conventional current flow
The flow of positive charge from
the positive to the negative terminal.
Conventional current is opposite to
electron flow.
Electron flow
The actual movement of electrons,
which flows from the negative to the
positive terminal.
Alternating Current vs Direct Current
Electric current flows in two ways as an alternating
current (AC) or direct current (DC). The main
difference between AC and DC lies in the direction in
which the electrons flow.
AC (Alternating Current) is an electric current that
periodically reverses direction. The voltage
alternates between positive and negative, which
means the flow of electrons changes direction.
DC (Direct Current) DC is an electric current that
flows in one direction only, maintaining a constant
voltage.
Rectification
Rectification is the process of converting Alternating Current (AC)
into Direct Current (DC). AC voltage periodically reverses direction,
while DC flows in only one direction. Many electronic devices require
a steady DC voltage, so rectification is necessary for power supplies.
Why Do We Need Rectification?
• AC is commonly used in power transmission
due to efficiency in long-distance
transmission.
• Most electronic circuits, like those in mobile
phones and computers, require DC.
• Rectification allows AC mains electricity to be
converted into usable DC power.
DIODE
A diode is a semiconductor device that
allows current to flow in one direction only. It
consists of P-type and N-type materials
forming a PN junction. The diode's main
function in rectification is to block the
negative half-cycle of AC, allowing only
positive cycles to pass.
Forward Bias:
When the anode is more positive than the cathode, the diode conducts
current.
Reverse Bias:
When the cathode is more positive than the anode, the diode blocks current.
DIODE
A diode is a semiconductor device that
allows current to flow in one direction only. It
consists of P-type and N-type materials
forming a PN junction. The diode's main
function in rectification is to block the
negative half-cycle of AC, allowing only
positive cycles to pass.
Forward Bias:
When the anode is more positive than the cathode, the diode conducts
current.
Reverse Bias:
When the cathode is more positive than the anode, the diode blocks current.
A rectifier is a circuit that converts AC to DC using diodes.
In order for a current to flow,
the circuit must be closed; in
other words, there must be an
uninterrupted path from the
power source, through the
circuit, then back to the power
source.
Remember that a circuit is the complete path of electrical energy. In
the circuit we have created here with the light bulb, wire and battery,
the battery provides the voltage, and the light bulb gives us resistance,
by slowing down the flow of charge and changing it into light. The
current flows through the battery, the light bulb and the wires.
What might happen if we
disconnect the switch?
The light goes off because the current has nowhere to flow.
This creates what we call an OPEN CIRCUIT. It is like an open
circle because there is a break in the line of flow.
OPEN AND CLOSED CIRCUIT
Open Circuit
An open circuit is a broken or incomplete
electrical path, meaning the current cannot flow
because there is a break in the circuit.
Closed Circuit
A closed circuit is a complete electrical
path where current can flow from the power
source (such as a battery or power supply)
through the components (like resistors, bulbs,
etc.) and back to the power source. In other
words, all parts of the circuit are connected, and
the electrical current has a continuous path to
flow.
All circuits need to have three basic
elements. These elements are a
Voltage source, conductive path and a
load. The voltage source, such as a
battery, is needed in order to cause the
current to flow through the circuit. In
addition, there needs to be a
conductive path that provides a route
for the electricity to flow. Finally, a
proper circuit needs a load that
consumes the power.
RESISTANCE
Electrical Resistance
Electrical resistance, or simply resistance, is the opposition of a material
to the flow of electric current. The SI unit of resistance is the ohm (Ω),
named after Georg Simon Ohm.
Most electrical connections make use of devices called resistors to
regulate the amount of current passing through a conductor.
Factors Affecting the Resistance of a Uniform Wire
There are four factors affecting the resistance of a uniform wire. These are crosssectional area, length, kind of material, and temperature.
Cross-Sectional Area
Resistance R varies inversely from the crosssectional area A of the wire. As the area increases,
the resistance decreases. Thus, a thick wire has
lesser resistance than a thin wire.
Length
The resistance of a wire is directly proportional to its
length. A longer wire has greater resistance than a
shorter wire of the same material and crosssectional area.
Factors Affecting the Resistance of a Uniform Wire
There are four factors affecting the resistance of a uniform wire. These are crosssectional area, length, kind of material, and temperature.
Temperature
Resistance and resistivity vary with temperature.
As temperature increases, resistance and
resistivity increase for conductors and decrease
for insulators and semiconductors. In special
alloys such as manganin(copper-manganese
nickel) and constantan(copper-nickel alloy), they
hardly
change
with
temperature.
For
superconductors, resistance and resistivity first
decrease as temperature decreases just like
ordinary conductors. But a certain critical
temperature, resistance and resistivity drop to
zero.
Factors Affecting the Resistance of a Uniform Wire
There are four factors affecting the resistance of a uniform wire. These are crosssectional area, length, kind of material, and temperature.
Material of the Wire
The effect of the kind of material on the resistance of
the wire is determined by its resistivity. Resistivity 𝜌 is
the reciprocal of conductivity. Conductors have
small resistivities, while insulators have large
resistivities.
The table below lists resistivity values for some
materials. Note that resistivity is dependent on
temperature.
The effect of the length, cross-sectional area, and material on
resistance may be written as:
𝑳
R=ρ
𝑨
Where:
R - is the resistance of the wire (in ohms, Ω)
ρ - is the resistivity of the material (in ohm-meters, Ω⋅m)
L - is the length of the wire (in meters, m)
A - is the cross-sectional area of the wire (in square meters, m2)
This formula shows that the resistance increases with the length of
the wire and decreases with a larger cross-sectional area. The
resistivity 𝜌, depends on the material the wire is made of.
EXAMPLE PROBLEM:
An insulated extension cord is made of a 1.5 m long copper rod with a
diameter of 2.3 mm.
(a) What is the resistance of the extension cord?
(b) If an aluminum wire of the same length will be used instead of copper,
what should be the diameter of the aluminum wire to have the same
resistance?
Given:
Lcopper = 1.5 m
dcopper = 2.3 x 10-3 m
𝜌copper = 1.72 x 10-8 Ω.m
𝜌aluminum = 2.75 x 10-8 Ω.m
The Measurement of Current, Voltage, and Resistance
The current, voltage, and resistance
in an electric circuit are measured
by an ammeter, voltmeter, and
ohmmeter, respectively. Most of the
time, these three measuring devices
are combined to form a multimeter,
which can be switched from one
measuring device to another.
AMMETER
An ammeter is a device used for
measuring current. It is always
connected in series with the circuit
element to which the current is to be
determined.
An
ammeter
is
connected by opening the circuit and
then inserting it in line or in series
with the circuit. An ammeter is a
circle with an uppercase letter A.
VOLTMETER
A voltmeter is a device that measures
the electromotive force or potential
difference between two points in a
circuit. A voltmeter is connected across
or parallel to the part of the circuit
element where potential difference is to
be determined. A voltmeter is
represented as a circle with an
uppercase V.
OHMMETER
An ohmmeter is a device used to measure the resistance of a component
or circuit. It is part of a family of tools known as multimeters, which can
also measure voltage and current. The primary function of an ohmmeter is
to measure the electrical resistance, which is expressed in ohms (Ω).
Safety Devices
Many safety devices and features are considered
in the design of an electrical system in the house
or workplace. Household circuitry consists of
several connected circuits parallel to the main
power line. In turn, each circuit contains several
parallel outlets. Because of this, appliances at
home may be used independently of each other.
However, using too many appliances at the same
time may result in circuit overload. Electrical
overloads happen when the amount of
electricity passing through a circuit exceeds the
capacity of the circuit. The wires may get heated
and cause fire.
Safety Devices
To prevent overloading, fuses or circuit breakers
are inserted (in series) in circuits. A fuse consists
of a high-resistance strip of alloy that melts
readily. For instance, a 15 A fuse melts if the
current exceeds 15 A. When the fuse wire melts,
it blows up.
A circuit breaker, on the other hand, is a large
switch that is automatically opened by an
electromagnet when the current is large. The fuse
blows up and the circuit breaker trips when the
current is excessive. This disrupts the entire
circuit, thus preventing the current from flowing
to the appliances connected to it. A blown-up
fuse can never be used again; a breaker that trips
can be reset.
Safety Devices
Most electrical appliances use a three-prong plug in
their power cords. The two principal flat wires, called live
and neutral, are the current-carrying wires and the third
prong (round prong) is a safety ground wire that carries
no current. It is grounded to prevent electric shock in
case a live wire accidentally touches a metal part of the
appliance.
In addition, electrical appliances are
provided with a green or yellow ground
wire. This is usually connected to the
casing of appliances. If the live wire comes
in contact with the casing, most of the
current takes the low-resistance path
through the appliance to the ground.
Effects of Current on the Human Body
The extent of injury depends on the amount of electric current that flows
through the body, time of exposure, and path taken by the current. The
human body is a good conductor because it is composed of 70 percent
water.
However, dry skin offers a resistance of as high as 100,000 Ω to 500,000 Ω
(100 kΩ – 500 kΩ) under normal conditions. However, if the skin is wet,
resistance can drop to 1,000 Ω – 10,000 Ω, allowing dangerous currents to
flow. The longer the time of exposure to the current, the greater the
damage.
Effects of Current on the Human Body
The source of current must be
quickly shut down. A few seconds
of delay spells the difference
between life and death. The parts
of the body that are more sensitive
to current are the brain, heart,
chest muscles, and nerves
regulating
respiration.
The
dangerous path of current would
be hand to hand and left hand to
either foot.
The effects of current on a person are shown in the table below.
OHM’S LAW
OHM’S LAW
Ohm's law is the most important, basic law of
electricity. It defines the relationship between the
three fundamental electrical quantities: current,
voltage, and resistance.
When a voltage is applied to a circuit containing
only resistive elements (i.e. no coils), current
flows according to Ohm's Law.
“Ohm's law states that the electrical current (I) flowing in a circuit is proportional
to the voltage (V) and inversely proportional to the resistance (R).”
𝑉
I=
𝑅
QUANTITY
OHM'S
LAW
SYMBOL
VOLTAGE
V
CURRENT
I
RESISTANCE
R
UNIT OF
ROLE IN
MEASURE
CIRCUITS
(ABBREVIATION)
IN CASE YOU'RE WONDERING:
Volt (V)
Pressure that
triggers electron
flow
Ampere, amp (A) Rate of electron
flow
V = electromotive force (old-school
term)
Ohm (Ω)
Ω = Greek letter omega
Flow inhibitor
I = intensity
VOLTAGE
The difference in potential energy of the charges is potential difference or
voltage. Voltage is the driving force in electric circuits and is what establishes
the flow of free electrons in a conductive material or the electric current.
V= 𝐼𝑅
SOME COMMON VOLTAGE SOURCES:
• Battery – A type of voltage source that converts chemical energy into electrical
energy.
• Electronic power supply – It converts the AC supply from wall outlet to a constant
DC voltage.
• Solar cell – The operation of solar cell is based on the principle of “photovoltaic
action”, that light is converted directly into electrical energy.
• Generator – It converts mechanical energy into electrical energy using a principle
called “electromagnetic induction”.
CURRENT
Voltage provides energy to electrons which allows them
to move through a circuits. This movement of electrons is
the current, which results in work being done in an
electric circuit. Electric current is flow of electrons in a
conductor.
RESISTANCE
𝑽
I=
𝑹
When there is current in a material, the free electrons move through the material and occasionally
collide with atoms. This collision cause the electrons to lose some of their energy and thus their
movement is restricted. This restriction varies and is determined by the type of material. The
property of a material that restricts the flow of electrons is called, resistance. R is the resistance of
the resistor, measured in Ohms (Ω)
𝑽
R=
𝑰
EXAMPLE 1: Voltage (E) and resistance (R) are known.
I = V/R
I = 12V/6Ω
I=2A
EXAMPLE 2: Voltage (E) and current (I) are known.
R = V/I
I = 24V/6A
I=4Ω
EXAMPLE 3: Current (I) and resistance (R) are known.
What is the voltage?
V = IR
V = (5A)(8 Ω)
V = 40V
RESISTORS
Electronic components that are specifically designed to have a certain amount of
resistance. The Principal applications of resistors are to limit current; to divide voltages;
and in certain cases, to generate heat.
Resistance values of the resistors may be fixed or variable. Potentiometers, lightdependent resistors, thermistors, and wire-wound, rheostats have variable resistances.
Mettalized film resistors, carbon resistors, wire wound resistors, and chip resistors have
fixed values.
Resistor Schematic Symbol
Two sets of symbols are used to
represent resistors: one by the
International
Electrotechnical
Commission (IEC) and another by
the American National Standards
Institute (ANSI). These symbols
are shown in the table.
ANSI STANDARD
IEC STANDARD
EXAMPLE: 4 BAND RESISTOR
100 Ω ±5%
MEASURING RESISTOR
WITH AN OHMMETER
To measure a resistor using an ohmmeter, first
turn off the power, set the meter to the
resistance (Ω) mode, connect the probes to
both ends of the resistor, and read the
displayed resistance value.
The resistance of all components connected in
parallel with a component being tested affects
the resistance reading, usually lowering it.
Always check the circuit schematic for parallel
paths.
VOLTAGE DIVIDER
A voltage divider is a simple circuit consisting
of two resistors connected in series. It divides
the input voltage into smaller, proportional
voltages, which can be useful for obtaining a
lower voltage from a higher voltage source.
Vout = IR2
I = Vin / Rtotal
Substituting;
𝑅2
Vout = 𝑅𝑇𝑜𝑡𝑎𝑙 (𝑉𝑖𝑛)
Applications of Voltage Dividers
Voltage dividers are widely used in various applications:
• Adjusting signal levels: If you want to reduce the voltage to a safer
level for an LED or other component.
• Measuring voltages: In sensors, where the voltage needs to be scaled
down before it’s fed into an analog-to-digital converter (ADC).
• Creating reference voltages: For circuits requiring a known reference
voltage, such as in amplifiers or comparator circuits.
EXAMPLE PROBLEM:
Voltage dividers are widely used in various applications:
• Adjusting signal levels: If you want to reduce the voltage to a safer
level for an LED or other component.
• Measuring voltages: In sensors, where the voltage needs to be scaled
down before it’s fed into an analog-to-digital converter (ADC).
• Creating reference voltages: For circuits requiring a known reference
voltage, such as in amplifiers or comparator circuits.
SERIES AND PARALLEL
CIRCUITS
SERIES AND PARALLEL CIRCUITS
Components of an electrical circuit or electronic circuit
can be connected in series, parallel, or series-parallel.
The two simplest of these are called series and parallel
and occur frequently.
Components connected in series are connected along
a single conductive path, so the same current flows
through all of the components but voltage is dropped
(lost) across each of the resistances. In a series circuit,
the sum of the voltages consumed by each individual
resistance is equal to the source voltage.
Components connected in parallel are connected
along multiple paths so that the current can split up;
the same voltage is applied to each component.
SERIES AND PARALLEL CIRCUITS
“In a series circuit, the current that flows through each of the
components is the same, and the voltage across the circuit is the
sum of the individual voltage drops across each component.”
“ In a parallel circuit, the voltage across each of the components
is the same, and the total current is the sum of the currents
flowing through each component.”