#### Transcript Lecture 3 - Harding University

```Series and Parallel
Circuits
Kirchoff ’s Voltage and
Current Laws
Circuits 1
Fall 2005
Harding University
Jonathan White
Outline


Node definition
KCL


KVL




The sum of voltages around a closed loop is 0.
Series circuits


The current entering a node is equal to the current leaving a node.
Req is always greater than R1 and R2
Voltage Dividers
Parallel circuits


Resistors in parallel follow the equation Req = (R1*R2)/(R1+R2).
Req is always less than R1 and R2
Nodes

A node is where 2 or more elements meet.



For now, and element can be a resistor, a voltage
source, or a current source.
Each point in the node must be electrically the
same.
Exp:
Kirchoff ’s Current Law

A fundamental law of nature, like the Law of
Conservation of Mass.



KCL is the conservation of charge – charge can
neither be created or destroyed.
KCL definition: The sum of all currents
entering a node is equal to the sum of all
currents leaving the node.
KCL holds for every node in a network and it
works at every point in time.
KCL

Write equations for the current in each of the
nodes in the circuit below:
Kirchoff ’s Voltage Law

A fundamental law of nature, like the Law of
Conservation of Energy.

KVL is the conservation of electrical energy –
electrical energy can neither be created or destroyed,
only transferred.
KVL – 2
1.
2.
3.
4.
5.
6.
As the charge moves from the top of the battery to
the top of Element #1 (along the wire shown in
purple), how much energy does the charge lose?
As the charge moves from the top of Element #1
through Element #1 to the bottom of element #1,
how much energy does the charge lose?
As the charge moves from the bottom of Element
#1 to the top of Element #2, how much energy
does the charge lose?
As the charge moves from the top of Element #2
through Element #2 to the bottom of element #2,
how much energy does the charge lose?
As the charge moves from the bottom of Element
#2 to the bottom of the battery, how much energy
does the charge lose?
As the charge moves from the bottom of the
battery through the battery to the top of the
battery, how much energy does the charge lose?
KVL - 3

What is Vb equal to?

KVL definition: the sum of
voltages around a closed loop is
0.
KVL - 4

Write all the KVL equations for the circuit
below:
Series Resistance


2 devices are said to be in series when the same current
physically flows through both.
 Current flows into one element, through the element, out of
the element into the other element, through the second
element and out of the second element. No part of the
current that flows through one resistor "escapes" and none is
You see series resistance everyday
Series Resistance - 2

Consider the simplest series resistance:

What is Vs ?
The equivalent resistance for resistors in series is
always the sum of the individual resistors.

Voltage Dividers



Used as volume controls in electronic devices
 Provides a continuous sound spectrum, i.e., not digital.
Used in RC combinations to filter out input noise in devices
such as tachometers and …
A voltage divider looks like this:
Voltage Dividers - 2




How much current flows through Ra
and Rb ? Use Ohm’s Law.
What is Vout ?
As Rb goes to 0, what’s the value of
Vout ? Rb is then physically like what?
As Rb goes to ∞, what’s the value of
Vout ? Rb is then physically like what?
Parallel Resistors

2 resistors are in parallel if the same physical
voltage appears across each resistor.

Each resistor provides its own path for the flow of
current. If the resistors have different resistance
values, they will carry different amounts of current,
each in accordance with Ohm's Law.
Parallel Resistors - 2


Consider the simplest
parallel resistance to the
right. What is Ip?
In parallel resistors, the
equivalent resistance is
always lower than either of
the resistors.
```