FUNDAMENTALS OF ELECTRIC CIRCUITS
EE 318
Dr. ARVIND TIWARI
B1-S-026
arvindtiwari@qec.edu.sa
0557028960
DEPARTMENT OF ELECTRICAL ENGINEERING,
COLLEGE OF ENGINEERING
AL-QASSIM UNIVERSITY
Two types of current are there: DC and AC. One is direct current (dc), in which ideally the flow of charge (current)
does not change in magnitude (or direction) with time. The other is sinusoidal alternating current (ac), in which the
flow of charge is continually changing in magnitude (and direction) with time.
The current is limited only by the resistor R. The higher the
resistance, the less the current, and conversely, as determined by
Ohm’s law.
The direction of conventional current flow (Iconventional)
is opposite to that of electron flow(Ielectron).
For single-voltage-source dc circuits, conventional flow always
passes from a low potential to a high potential when passing
through a voltage source,
However, conventional flow always passes from a high to a low
potential when passing through a resistor for any number of voltage
sources in the same circuit
SERIES RESISTORS
Resistor has only two terminals to connect in a configuration—it is therefore
referred to as a two-terminal device
One terminal of resistor R2 is connected to resistor R1 on one side, and the remaining
terminal is connected to resistor R3 on the other side, resulting in one, and only one,
connection between adjoining resistors. When connected in this manner, the resistors
have established a series connection.
The total resistance of a series configuration is the sum of the resistance levels
For any number (N) of resistors,
The more resistors we add in series, the greater the resistance, no matter what their value.
where resistors are the same value
where N is the number of resistors in series of value R
The total resistance of resistors in series is unaffected by the order in which they are connected
SERIES CIRCUITS
A circuit is any combination of elements that will result in a continuous flow of charge, or current, through
the configuration.
The direction of conventional current in a series dc circuit is such that
it leaves the positive terminal of the supply and returns to the
negative terminal
The current is the same at every point in a series circuit
In any configuration, if two elements are in series, the current must be the same. However, if the current is
the same for two adjoining elements, the elements may or may not be in series.
The polarity of the voltage across a resistor is determined by
the direction of the current
Current entering a resistor creates a drop in voltage with
the polarity indicated
Reverse the direction of the current, and the polarity will reverse
The magnitude of the voltage drop across each resistor can then be found by applying Ohm’s law using only the
resistance of each resistor
VOLTAGE SOURCES IN SERIES
Voltage sources can be connected in series to increase or decrease the total voltage applied to a system.
The net voltage is determined by summing the sources with the same polarity and subtracting the total of the
sources with the opposite polarity. The net polarity is the polarity of the larger sum.
KIRCHHOFF’S VOLTAGE LAW
Define a closed path of investigation, start at one point in the network, travel through the network, and back to the
original starting point. The path does not have to be circular, square, or any other defined shape; it must simply provide
a way to leave a point and get back to it without leaving the network.
The algebraic sum of the potential rises and drops around a closed path (or closed loop) is zero.
The term algebraic simply means paying attention to the signs that result in the
equations as we add and subtract terms.
The applied voltage of a series dc circuit will equal the sum of the
voltage drops of the circuit
The sum of the voltage rises around a closed path will always equal the sum of the voltage drops.
There is no requirement that the followed path have charge flow or current.
In cases where polarity is unknown, simply assume a polarity. If the answer is negative, the magnitude of the
result is correct, but the polarity should be reversed.
VOLTAGE DIVISION IN A SERIES CIRCUIT
The voltage across series resistive elements will divide as the magnitude of the resistance levels.
In a series resistive circuit, the larger the resistance, the more of the applied voltage it will capture.
The ratio of the voltages across series resistors will be the same as the ratio of their resistance levels.
Voltage Divider Rule (VDR)
The voltage divider rule (VDR) permits the determination of the voltage
across a series resistor without first having to determine the current of the circuit
.
First, determine the total resistance as follows:
Apply Ohm’s law to each resistor:
The resulting format for V1 and V2 is
The voltage across a resistor in a series circuit is equal to the value of that resistor times the total applied
voltage divided by the total resistance of the series configuration.
The voltage divider rule can be
extended to the voltage across two or
more series elements if the resistance
in the numerator is expanded
to include the total resistance of the
series resistors across which
the voltage is to be found (R).
USING KVL:
USING KVL FOR LOOP 1:
PARALLEL RESISTORS
Two elements, branches, or circuits are in parallel if they have two points
in common.
For resistors in parallel
The total resistance is determined from the following equation
Since G = 1/R, the equation can also be written in terms of conductance
levels as follows
The total resistance of parallel resistors is always less than the value
of the smallest resistor.
if the smallest resistor of a parallel combination is much smaller than the other parallel resistors, the total
resistance will be very close to the smallest resistor value.
The total resistance of parallel resistors will always drop as new resistors are added in parallel, irrespective
of their value.
For N equal resistors in parallel,
The total resistance of N parallel resistors of equal value is the
resistance of one resistor divided by the number (N) of parallel resistors.
For two parallel resistors, the total resistance is
The total resistance of two parallel resistors is simply the product of their values divided by their sum
Parallel resistors can be interchanged without affecting the total resistance.
PARALLEL CIRCUITS
A parallel circuit can now be established by connecting a supply across
a set of parallel resistors
The voltage is always the same across parallel elements
if two elements are in parallel, the voltage across them must be the
same. However, if the voltage across two neighboring elements is the
same, the two elements may or may not be in parallel.
The source current can be determined using Ohm’s law:
Since the voltage is the same across parallel elements, the current through each resistor
can be determined using Ohm’s law.
For single-source parallel networks, the source current (Is) is always equal to the sum of the individual
branch currents.
For a parallel circuit, the source current equals the sum of the branch currents, while for a
series circuit, the applied voltage equals the sum of the voltage drops.
For parallel resistors, the greatest current will exist in the branch with the least resistance.
KIRCHHOFF’S CURRENT LAW
The algebraic sum of the currents entering and leaving a junction (or
region) of a network is zero.
The sum of the currents entering a junction (or region) of a network
must equal the sum of the currents leaving the same junction (or
region).
In equation form,
with Ii representing the current entering, or “in,” and Io representing the
current leaving, or “out.”
the term node is commonly used to refer to a junction of two or more branches.
In cases where direction of current is unknown, simply make an assumption about the direction and then
check out the result. If the result is negative, the wrong direction was assumed.
If the result is positive, the correct direction was assumed. In either case, the magnitude of the current
will be correct.
CURRENT DIVIDER RULE For finding the current through a resistor in a parallel circuit.
The current through any branch of a parallel resistive network is equal to the total resistance of the
parallel network divided by the resistor of interest and multiplied by the total current entering the
parallel configuration.
• For two parallel elements of equal value, the current will divide equally.
• For parallel elements with different values, the smaller the resistance, the greater the share of input
current.
• For parallel elements of different values, the current will split with a ratio equal to the inverse of their
resistor values.
The current IT can then be determined using Ohm’s law
Since the voltage V is the same across parallel elements
Substituting for V in the above equation for IT
Solving for Ix , the final result is the current divider rule
For a parallel network, the current through the smallest resistor will be very close to the total
entering current if the other parallel elements of the configuration are much larger in magnitude.
Since RT and IT are constants, for a particular configuration the larger the value of Rx (in the denominator),
the smaller the value of Ix for that branch, confirming the fact that current always seeks the path of least
resistance.
Two Parallel Resistors
For two parallel resistors, the current through one is equal to the
other resistor times the total entering current divided by the sum of
the two resistors.
VOLTAGE SOURCES IN PARALLEL
Because the voltage is the same across parallel elements,
Voltage sources can be placed in parallel only if they have the same voltage.
The primary reason for placing two or more batteries or supplies in parallel
is to increase the current rating above that of a single supply
OPEN AND SHORT CIRCUITS An open circuit is two isolated terminals not connected by an
element of any kind
An open circuit can have a potential
difference (voltage) across its
terminals, but the current is always
zero amperes
A short circuit is a very low resistance, direct connection between two
terminals of a network
A short circuit can carry a current of a level determined by the
external circuit, but the potential difference (voltage) across its
terminals is always zero volts.
SERIESPARALLEL
NETWORKS
A series-parallel
configuration is one that
is formed by a
combination of series
and
parallel elements.
FIND THE UNKNOWN VOLTAGE Vx FOR FIG. 1 AND FIG. 2
FIG. 1
FIG. 2
USING KVL:
1.
2.
Determine resistor R1 to implement the division of
current shown
FIND THE CURRENT IN ALL THE BRANCHES AND THE SOURCE CURRENT?