Chapter 5 & 6
Dr. Farid Farahmand
CET 236
Outline
Identify a series/parallel circuit
 Determine the current and voltage in a
circuit
 Determine total resistance
 Apply Ohm’s law
 Apply Kirchhoff’s voltage law

Series Circuit

A series circuit provides only one
path for current between two
points


current is the same through each
series resistor.
Find the total resistance in a series
circuit

sum of the resistances of each
individual series resistor.
RT = R1 + R2 + R3 + . . . + Rn
Ohm’s Law in Series Circuits



If you know the total current, you can find the voltage drop across
any of the series resistors by using:
VR = ITR
The polarity of a voltage drop across a resistor is positive at the
end of the resistor that is closest to the positive terminal of the
voltage source
An open in a series circuit prevents current; and, there is zero
voltage drop across each series resistor.

The total voltage appears across the points between which there is
an open
+
-
Voltage Sources in Series

When two or more voltage sources are in
series, the total voltage is equal to the
the algebraic sum (including polarities of
the sources) of the individual source
voltages.
Kirchhoff’s Voltage Law (KVL)

The sum of all the voltage
drops around a single closed
loop in a circuit is equal to the
total source voltage in that
loop.
VS = V 1 + V 2 + V 3 + … + V n
Or
VS - V1 - V2 - V3 = 0

Since each resistor has the
same current, the voltage
drops are proportional to the
resistance values.
Vx = (Rx/RT)VS
Power in a Resistive Circuit

The total amount of power in a series/parallel
resistive circuit is equal to the sum of the
powers in each resistor in series.
PT = P1 + P2 + P3 + . . . + Pn
Remember
Px = Vx.Ix

The amount of power in a resistor is important

the power rating of the resistor must be high
enough to handle the expected power in the circuit.
Open and Short Circuit

When an open occurs in a
series circuit, all of the source
voltage appears across the
open.
 The most common failure
in a series circuit is an
open.

When a short occurs a
portion of the series
resistance is bypassed, thus
reducing the total resistance.
 A short in a series circuit
results in more current
than normal.
What is the current when there
is no short?
What is the current when the
circuit is shorted?
Open and Short Circuit

When an open occurs in a
series circuit, all of the source
voltage appears across the
open.
 The most common failure
in a series circuit is an
open.

When a short occurs a
portion of the series
resistance is bypassed, thus
reducing the total resistance.
 A short in a series circuit
results in more current
than normal.
Let’s Examine Parallel Circuits!
Resistors in Parallel


Each current path is called a branch.
 A parallel circuit is one that has more than one branch.
The voltage across any given branch of a parallel circuit is equal
to the voltage across each of the other branches in parallel
Two Branches
Kirchhoff’s Current Law (KCL)

Two ways of stating it:


The sum of the currents into a
junction (total current in) is equal
to the sum of the currents out of
that junction (total current out).
The algebraic sum of all the
currents entering and leaving a
junction is equal to zero.
IIN(1) + IIN(2) + . . . + IIN(n) = IOUT(1) + IOUT(2) + . . . +IOUT(m)
Total Parallel Resistance

When resistors are connected in parallel, the
total resistance of the circuit decreases.
 The total resistance of a parallel circuit is
always less than the value of the smallest
resistor.
1/RT = 1/R1 + 1/R2 + 1/R3 + . . . + 1/Rn
or
RT = R1||R2||R3||R4||R5….Rn
What is the total resistance in a parallel circuit with 2 resistors?
RT = R1R2/(R1 + R2)
Current in Parallel Circuits

The total current
produced by all current
sources is equal to the
algebraic sum of the
individual current
sources.
 A parallel circuit acts as
a current divider
because the current
entering the junction of
parallel branches
“divides” up into several
individual branch
currents.
I1=Vs/R1 = IT.RT/R1
I1 = (R2/(R1 + R2))IT
I2 = (R1/(R1 + R2))IT
Given IT, find I1 and I2!
Circuit Example: How does it work?