# 1.03 Voltage Dividers

Voltage Dividers take an input voltage and gives you a smaller, fractional output voltage. This can be useful for volume control or when interfacing between logic circuits that run at 5V with new/lower power devices that run at 3.3V.

A voltage divider is a simple circuit made up of only two resistors (R1 & R2 in the diagram below).

# 1.02 Relationship between voltage and current: resistors

Art of Electronics 2nd Edition p 4-7

What you MUST learn

Resistance (represented in formulas as “R”) measured in Ohms which is represented using the symbol:

Resistance is the relationship between Current (I) and Voltage (R).

This relationship is defined by Ohm’s law:  R = V/I.

Circuit diagrams represent resistors as

Resistors in Series: (Always bigger)

R= R1 + R2

Resistors in Parallel: (Always smaller)

R = (R1*R2)/(R1+R2)

Shortcut #1:

A large resistor in series with a small resistor has the resistance of the larger one, roughly.

A large resistor in parallel with a  small resistor has the resistance of the smaller one, roughly.

Try to develop an intuitive sense of the voltage and current in the parts of the circuit.  Do not try to calculate to be extremely precise because the precision of the components will make this pointless.  Also, good circuit design should be tolerant of variations.

Power:

P=IV

Using Ohm’s law you get:

P=(I^2)R

P=(V^2)/R

Things good to learn

The inverse of resistance is conductance (represented by “G” in formulas)  G=1/R

Restatement of Ohm’s law:  I=GV

Conductance is measured in siemens

siemens is also known as mho (ohm spelled backwards)

# 1.01 Voltage and Current

Art of Electronics 2nd edition, pages 2-4

Overview

Voltage & Current describe two aspects of electronic circuits that are fundamental to understand and on which everything else will build on.

What you MUST learn

Voltage refers to a force that when applied across a circuit causes current to flow.  Voltage is measured in volts (using the symbol V) also called a “potential difference”.  It is measured across two points in a circuit.  A joule of work is needed to move a coulomb of charge through a potential difference of one volt. A coulomb is the charge of about 6×10^18 electrons.

Current (symbol: I) is the measure of electronics through a point in a circuit.  It is measured in amperes (amps) (symbol: A).  1 ampere (amp) is 1 coulomb of charge passing through a point per second.

Conservation of Charge:  Kirchhoff’s current law

The sum of currents into a point or node is equal to the sum of the currents out of a point or node.  This is referred to as Kirchhoff’s current law.

Kirchhoff’s voltage law

The sum of voltage drops through one branch of a circuit will equal the sum of voltage drops across the other branches of the circuit.

P=VI

Power (work per unit time), measured in watts.  (1 W = 1 J/s)

P=VI = (work/charge) x (charge/time) = work/time

P=VI= (1 joules/1 coulomb) x (1 coulomb/1 second) = 1 joules/second = watt.

Things good to learn

Voltage is usually written with the symbol V but sometimes E is used.   Voltage is also called a “potential difference” or electromotive force (EMF).

Prefixes:

 Multiple Prefix Symbol 10^12 tera T 10^9 giga G 10^6 mega M 10^3 kilo k 10^(-3) milli m 10^(-6) micro µ 10^(-9) nano n 10^(-12) pico p 10^(-15) femto f

When abbreviating a unit with a prefix, the unit follows the multiplier with no space and the unit is capitalized.  However, no capitalization for both prefix and unit when spelled out.  1mW = 1 milliwatt

1 MV = 1 megavolt

Related information and insights from my other books

Introductory Circuit Analysis 9th edition – chapter 2

Structure of the atom:

nucleus is made up of protons (that have a positive charge) and neutrons that have a negative charge.  The proton and neutron are relatively the same mass.  But the electron is considerably smaller (1836 times smaller) than the proton but has a negative charge that is equal to the positive charge of the proton.

Other things of interest

If you need more help

Voltage

Current

Joule

If you wanted to know

Who defined:

Voltage

Volt

Current

amp

joule

watt

multiplier prefixes

People who contributed:

Watt

# Preparing for my journey through “The Art of Electronics”

“The Art of Electronics” by Horowitz and Hill is the definitive guide to Analog and Digital electronics.  I had bought the 2nd edition over a decade ago, with the intention of going through it.  But this year is going to be the year.  And I am hoping that you will help me.

My plan is to go through a section a day, and to write a short blog post summarizing what I learned.  I have collected several electronics books, and I plan to make reference to them as I go on this journey.  These include:

In addition to a brief summary of what I learn from that section, I plan to create a video post, create additional exercises, and assemble related circuits.  I am hoping that it will be an exciting adventure, and that by having to produce a daily blog post, I will have the discipline to see it through.  And should I stumble, hopefully an encouraging comment or email from you will nudge me back on the path.

First thing is that I need some help by those that are familiar with Electronics.  I am an Amateur with hopes of achieving proficiency.  I do not want my struggles to cause problems for others following along.  Therefore, I would like to have someone knowledgeable review my notes before I publish them on this blog.  If you would be willing to help out, then please email me at nathan.price@gmail.com.  Let me know how much you would be willing to help out.  I figure each blog post would take 15 minutes or so to review.   I would like to give you credit for reviewing, but if you want to remain anonymous, then that is fine too.