Circuitry

General Physics 2
 Chapter Objectives
▪ Identify the symbols used for electric circuit diagrams.
▪ Understand the difference between current, voltage, and resistance.
▪ Determine the factors which affects electrical resistance.
▪ Apply Ohm’s law to circuit problems
▪ Understand the importance of resistors
▪ Apply Kirchoff’s current law (KCL) and Kirchoff’s voltage law (KVL) to circuits
▪ Differentiate series circuits from parallel circuits
▪ Calculate the equivalent resistance, current, and voltage from a series, a parallel, or a
combined circuit
▪ Calculate the electric power
Electric Circuit
Electric Circuits
The electric circuits are closed-loop or paths, forming a
network of electrical components where electrons can flow.
This path is made using electrical wires and is powered by a
source, like a battery. The start of the point from where the
electrons start flowing is called the source, whereas the point
where electrons leave the electrical circuit is called the
return.
• An electrical circuit is complete only when there is at
least one closed loop from the positive to the negative
end. This is the simplest form of an electric circuit.
• A complete circuit is an electric circuit in which
electricity successfully flows throughout the whole loop;
in other words, electricity is flowing from the power
source onto a component then back to the power
source again.
• An open circuit is when the flow of electricity is
discontinuous at a certain point.
• If the wire used were damaged or loose, it is known as a
short circuit.
Electric Current
Electric Current: The Flow of Charge
Electric Current: The Flow of Charge
▪ Electric Current is the rate of flow of electrons in a conductor.
The SI Unit of electric current is the Ampere.
▪ Electrons are minute particles that exist within the molecular
structure of a substance. Sometimes, these electrons are
tightly held, and other times they are loosely held. When
electrons are loosely held by the nucleus, they are able to
travel freely within the limits of the body. Electrons are
negatively charged particles hence when they move, a
number of charges moves, and we call this movement of
electrons as electric current. It should be noted that the
number of electrons that are able to move governs the
ability of a particular substance to conduct electricity.
The positive and negative terminals in a battery can be
imagined as two oppositely charged plates with an electric
field in between from the positive to the negative.
It would require work to move a positive test charge from a
negative terminal to positive terminal, increasing the
electric potential energy.
In this sense, the positive terminal is the high potential and
the negative is the low potential.
Therefore, a positive charge would naturally move from the
positive terminal, across the loop, to the negative terminal.
Mathematically, the electric current I is expressed as:

𝑸
𝑰=
𝒕
Where Q is the amount of charge in Coulombs and t
is the time in seconds.
he magnitude of electric current is measured
in coulombs per second. The SI unit of electric
current is Ampere and is denoted by the letter A.
Ampere is defined as one coulomb of charge
moving past a point in one second.
Conventional Current flow Vs Electron Flow
Conventional Current flow Vs Electron Flow
Conventional Current Flow
The conventional current flow is from the positive to the
negative terminal and indicates the direction in which
positive charges would flow.
Electron Flow
The electron flow is from negative to positive terminal.
Electrons are negatively charged and are therefore
attracted to the positive terminal as unlike charges
attract.
Sample Problem
Calculate the current of a 5C charge if it moves across a 10mm long wire at 5s.
Solution:

𝑄
𝐼=
𝑡

5𝐶
𝐼= = 1 𝐶/𝑠
5𝑠

𝐼 =1𝐴
There are two types of electric current known as alternating current
(AC) and direct current (DC). The direct current can flow only in one
direction, whereas the alternating direction flows in two directions.
Direct current is seldom used as a primary energy source in
industries. It is mostly used in low voltage applications such as
charging batteries, aircraft applications, etc. Alternating current is
used to operate appliances for both household and industrial and
commercial use.

The device used to measure the current of a circuit is called the

ammeter.
Electrical Resistance
 Electric Resistance
As electrons move across the wire, they collide with the atoms
of the wire. These collisions cause the direction of the
movement of the atoms to change, hindering the flow of
charges across the wire. As a result, these collisions cause
some loss of the electrical energy of the mobile electrons.
Nevertheless, most of the electric energy is lost as these
charges move to an electric device. These hindrance to the
flow of charges across the wire is called the resistance.
 Electric Resistance
When an electric current flows through a bulb or any
conductor, the conductor offers some obstruction to the
current and this obstruction is known as electrical
resistance and is denoted by R. Every material has an
electrical resistance and this is the reason why
conductors give out heat when current passes through it.
Electric Resistance
The amount of resistance of a certain material depends
on four main variables: the length, the cross-sectional
area, the nature of material, and the temperature.
 Length
The longer the length of a wire, the greater is the
resistance. In other words, the resistance of a wire is
proportional to its length L.
𝑹∝𝑳
Since the cause of hindrance of motion of the charges is
due to the collisions they experience along the wire,
when charges would likely experience more collisions as
the length of the wire increases.
 Cross-sectional Area
The resistance R of a wire is inversely proportional to its
cross-sectional area A.
𝟏
𝑹∝
𝑨
The flow of charges can be visualized as water flowing
through a pipe. A water flows through a pipe, the water
experience friction on the surface of the pipe. The larger
the area of the pipe, less friction will be experienced by
the water. Similarly, charges will experience less
resistance in wider wires.
 Nature of Material
Each metal has individual characteristics which separate it
from other materials. There are metals which are better
conductors of electricity than others. For example, copper if
better conductor than lead. Then, there are those materials
which have high resistance such as glass and rubber. This
property of materials is specified by the material’s resistivity.
𝟏
𝑹=𝝆
𝑨
Where 𝝆 is the resistivity in units of ohm-meter Ω ∙ 𝑚 . The
ohm is the unit of electrical resistance and is represented by
the omega symbol.
It was named aster German physicist, Georg Ohm.
 Temperature
Another factor which affects the resistance of materials, but
is often neglected, is the temperature. As the temperature
increases, the rate of motion of the particle increases as well,
resulting in an increase in the collision of the particles within
the wire.
This, in effect, would increase in the temperature for it to have
a great impact on the resistance. However, there are
material like silicon which experience a decrease in the
resistance as the temperature increases.
Ohm’s Law
Ohm’s law states the relationship between electric current and
potential difference. The current that flows through most
conductors is directly proportional to the voltage applied to it.
Georg Simon Ohm, a German physicist was the first to verify Ohm’s
law experimentally.
𝑉
In 1827, Georg Ohm formulated the equation: 𝐼 =
𝑅
Which described the relation between the voltage V, the current I,
and the resistance R.
Ohm’s Law Applications
The main applications of Ohm’s law are:
• To determine the voltage, resistance or current of an electric
circuit.
• Ohm’s law maintains the desired voltage drop across the
electronic components.
• Ohm’s law is also used in DC ammeter and other DC shunts to
divert the current.
Example 1:
If the resistance of an electric iron is 50 Ω and a current of 3.2 A flows
through the resistance. Find the voltage between two points.
Example 2:
An EMF source of 8.0 V is connected to a purely resistive electrical
appliance (a light bulb). An electric current of 2.0 A flows through it.
Consider the conducting wires to be resistance-free. Calculate the
resistance offered by the electrical appliance.
Limitations of Ohm’s Law
Following are the limitations of Ohm’s law:

• Ohm’s law is not applicable for unilateral electrical elements

like diodes and transistors as they allow the current to flow
through in one direction only.
• For non-linear electrical elements with parameters like
capacitance, resistance etc. the ratio of voltage and current
won’t be constant with respect to time making it difficult to use
Ohm’s law.
Resistors
Resistance may seem to be an obstruction in the circuit
since it hinders the flow of the electric charges in a circuit.
However, there are many cases in which the resistance
across the circuit has to be increased.
Resistors
The amount of resistance for each resistor by the color code
imprinted on the resistor.
Typically, resistors have 4, 5, or 6 bands, each with specific
meaning:
• 4-band resistor: the first two bands represent the first and
second significant digits of the resistance value, the third
band is the multiplier, and the fourth band indicates the
tolerance.
• 5-band resistor: the first three bands represent the
significant digits, the fourth band is the multiplier, and the
fifth band indicates the tolerance.
• 6-band resistor: similar to 5-band resistor, but include an
additional band for the temperature.
Resistor Color Code
Color Digit Multiplier Tolerance
Black 0 x1

Brown 1 x 10 ±1%

Red 2 x 100 ±2%

Orange 3 x 1000

Yellow 4 x 10,000

Green 5 x 100,000 ±0.5%

Blue 6 x 1,000,000 ±0.25%

Violet 7 x 10,000,000 ±0.1%

Gray 8 ±0.05%

White 9

Gold = ±5% Silver = ±10% None = ±20%

What is the value of resistance of the following
resistors?

1. red-yellow-green-orange-gold
2. Brown-red-red-silver
3. White-orange-red-green-gold
4. Violet-black-brown-gold
Sample Problem:

A 9.0 V battery is connected to a resistor with a 4-band color

code of red-green-black-no color. Calculate the current across
the circuit.
𝑉
𝐼=
𝑅
Sample Problem:
Calculate the current across the circuit.
𝑉
𝐼=
𝑅

1. A 12.0 V battery to a resistor with a 4-band color code of

orange-red-green-gold.
2. A 10.5 V battery to a resistor with a 5-band color code of
violet-brown-red-orange-silver
3. A 25.0 V power source to a resistor with a 5-band color code
of green-yellow-white-yellow-no color
Gustav Robert Kirchhoff, a German physicist, was born on March 12, 1824, in
Konigsberg, Prussia. His first research topic was the conduction of
electricity. This research led to Kirchhoff formulating the Laws of Closed
Electric Circuits in 1845. These laws were eventually named after Kirchhoff
and are now known as Kirchhoff’s Voltage and Current Laws.

He was the first person to verify that an electrical impulse travelled at the
speed of light. Furthermore, Kirchhoff made a major contribution to the
study of spectroscopy, and he advanced the research into blackbody
radiation.
Kirchhoff's Laws for Electric Circuits
Kirchhoff’s circuit laws lie at the heart of circuit
analysis. With the help of these laws and the equation
for individual components (resistor, capacitor and
inductor), we have the basic tool to start analyzing
circuits.
Kirchhoff's Laws for Electric Circuits
In 1845, a German physicist, Gustav Kirchhoff, developed a pair of laws
that deal with the conservation of current and energy within electrical
circuits. These two laws are commonly known as Kirchhoff’s Voltage
and Current Law. These laws help calculate the electrical resistance of
a complex network or impedance in the case of AC and the current
flow in different network streams.
Kirchhoff's Laws for Electric Circuits

• Kirchhoff’s Current Law goes by several names: Kirchhoff’s First Law and Kirchhoff’s
Junction Rule. According to the Junction rule, the total of the currents in a junction is
equal to the sum of currents outside the junction in a circuit.
• Kirchhoff’s Voltage Law goes by several names: Kirchhoff’s Second Law and
Kirchhoff’s Loop Rule. According to the loop rule, the sum of the voltages around the
closed loop is equal to null.
Kirchhoff’s First Law or Kirchhoff’s Current Law
The total current entering a junction or a node is equal to the charge leaving
the node as no charge is lost.
Kirchhoff’s First Law or Kirchhoff’s Current Law

In the above figure, the currents I1, I2 and I3 entering the node is considered positive,
likewise, the currents I4 and I5 exiting the nodes is considered negative in values. This
can be expressed in the form of an equation:
I1 + I2 + I3 – I4 – I5 = 0
A node refers to a junction connecting two or more current-carrying routes like
cables and other components. Kirchhoff’s current law can also be applied to analyse
parallel circuits.
Kirchhoff’s Second Law or Kirchhoff’s Voltage Law
The voltage around a loop equals the sum of every voltage drop in the same
loop for any closed network and equals zero.
 Kirchhoff’s Second Law or Kirchhoff’s Voltage Law

When you begin at any point of the loop and continue in the same direction, note the
voltage drops in all the negative or positive directions and returns to the same point. It
is essential to maintain the direction either counterclockwise or clockwise; otherwise,
the final voltage value will not be zero. The voltage law can also be applied in
analyzing circuits in series.
When either AC circuits or DC circuits are analysed based on Kirchhoff’s circuit laws,
you need to be clear with all the terminologies and definitions that describe the circuit
components like paths, nodes, meshes, and loops.