2. Introduction to Circuits

To make an electric circuit, we will need to make electrical connections between wires, and between wires and components.

Making Connections Between Wires

One of the simplest ways to make connections between wires is to twist them together. It’s easiest to start by crossing the wires, so they both have to bend when you twist them against each other.

wire twist

You can also twist them in a line, which is known as a splice.

wire splice

Another simple way to join wires is with an alligator test lead. Test leads have clips at both ends that you apply to the wires. Sometimes test leads have poor electrical contacts between their wires and the clip. Measure their resistance with your multimeter, and if it is higher than 0.5Ω, either repair the test lead or throw it away.

alligator test lead

Most Basic Circuit

Now we are ready to build the most basic circuit. A battery and a resistor.

The chemistry in the battery pushes electrons from its positive side to its negative side. The negative side of the battery then donates electrons to the circuit. The positive charge on the positive side of the battery attracts electrons from the circuit. The chemistry inside the battery (mostly) keeps electrons from moving backward within the battery itself.

The rest of the circuit allows the current of electrons to flow from the negative side of the battery, through wires and components, to the positive side.

In this most basic circuit, electrons leave from the negative side of the battery, run through the resistor, where they encounter resistance to their flow, and then are received on the positive side of the battery.

most basic circuit

The schematic for the most basic circuit is here. 

The red wire coming from the battery holder is connected to the positive terminal of the series of batteries. The black wire is connected to the negative terminal. I have twisted the resistor so that one lead from it connects to the red wire (positive) and one connects to the black wire (negative). Electrons flow out the black wire, through the resistor, and back into the red wire to return to the battery, which pushes them through again and again.

When you connect this circuit, there will be a current flowing, but you can’t see electrons, so you can’t tell.

Measure Current in a Circuit

WARNING: Do not measure the current without a resistor in the circuit. You can damage your meter.

If you want to measure an electrical current, you need to install that imaginary plane so you can count the charge crossing it. You must break the circuit somewhere to insert the meter to count the current flow.

Measuring current in a circuit.

Measuring current in a circuit.

The schematic for measuring current is here. 

Does it matter where you insert the meter in the circuit? No. Anywhere in the loop, the electrons don’t have any place to go except along the conductive path, so the current is the same everywhere in a single loop. If you have branches that make other loops, the current is not the same everywhere in the entire circuit, but at least you can say that the electrons that enter any location and the electrons that leave that location have to add up to zero, or you’d be creating or destroying electrons, which is vastly beyond the power of a mere battery to do. Kirchhoff stated it clearly, so we call it Kirchhoff’s Current Rule.

Kirchhoff’s Current Rule:

The sum of all currents flowing into a node must equal the sum of the currents flowing out of that node.

A node is a location in any circuit. We measure current through that location by counting the electrons that flow through our meter when it is in current-measuring mode. 

Measure a Voltages in a Circuit

We measure voltages in a circuit by looking for a voltage difference between two locations in the circuit. Here we are measuring the voltage difference across the 200Ω resistor.

Measuring the voltage across the resistor.

Measuring the voltage across the resistor.

The schematic for this circuit is here. 

We can measure voltage between any two points in the circuit. Count the sources of voltage (batteries and power supplies) as positive and add their positive voltages together, and count the other components as negative (they use up voltage to do their jobs) and subtract their voltages from the supply voltages.

Measuring voltages to check Kirchhoff's Voltage Rule.

Measuring voltages to check Kirchhoff’s Voltage Rule.

The schematic for this circuit is here. 

The result will be 0V, because the energy you put into the circuit from the battery and the energy you use up in your components must be the same. If you do these measurements and don’t get a 0 result, look for other sources or sinks of energy that you may have overlooked. Ordinary wires have a little bit of resistance, so measure across them, too. Kirchhoff summarized the accounting of the voltages in the circuit, so we call it Kirchhoff’s Voltage Rule.

This simplified method of adding the voltages across power supplies and subtracting the voltages across unpowered components only works if the power supplies are all pushing in the same direction. The rigorously accurate way of applying Kirchhoff’s Voltage rule is to pick a point on the circuit, and go around the loop, adding voltages that are positive in the direction you are going around the loop, and subtracting ones that are negative in the direction you are going around the loop.

Kirchoff’s Voltage Rule:

The sum of all voltages around any loop in any circuit must be 0.


Power is the rate at which energy is produced or transmitted or used. We measure power in Watts. 1 Watt is equal to 1 Joule of energy per 1 second of time.


If we want to calculate the electrical power, which we need to know to make circuits that work, we do some algebra to work out that Power = Current × Voltage.

electrical power

The practical limit for most electronics components is power. How much heat per time can you safely dump into the device before parts of it melt and it ceases to function?

To calculate the power dissipated in a device, you need to know the voltage across the device and the current that flows through it. For the circuit shown in the photographs above, the current is 23mA = 0.023A, and the voltage across the resistor is 4.72V.

power dissipation

The power dissipated in the resistor is less than the 1/8 Watt = 0.125W maximum limit for that resistor, so the resistor will operate normally and will not be damaged.


There is a kind of component that only allows current to flow in one direction. The asymmetry of the symbol shows you which way it conducts. All diodes give off light, but some are designed specifically for that purpose, and are put in transparent cases to let the light out. Those we call Light Emitting Diodes, or LEDs.

Ordinary Diode

Ordinary Diode


Light Emitting Diode: LED

Light Emitting Diode: LED

(Update: There are new kinds of LEDs that have the positive and negative leads arranged differently than shown in the microscope image on the left. However, it is still true that the longer lead is the positive lead, and the flat on the case is on the side for the negative lead. In any case, if it lights up, then you have it installed in the correct polarity.)

Install the diode with the dark triangle pointing towards the source of electrons, and it will conduct. Install a diode with the dark triangle pointing away from the source of electrons, and it will not conduct.

A diode in a circuit, showing electron flow current.

A diode in a circuit, showing electron flow current.

Because people started making circuits before we knew about the structure of the atom, they chose the positive charge as the one that moves. That isn’t true, but all of Electrical Engineering is built around the notion of the flow of imaginary positive charge. Since in almost all circuits it does not make any practical difference whether you talk about “electrons flowing to the left” or “positive current flowing to the right”, we continue to use both the real electron current and the imaginary positive current when we discuss circuits. This is confusing. Here’s what the diode circuits look like when labelled with positive flow. Note that the circuits schematics look the same, and the two circuits function the same. The circuit on the left has a flow of current. In the circuit on the right no current flows. Only the arrows indicating the direction of current flow have changed directions.

A diode in a circuit, showing imaginary positive current.

A diode in a circuit, showing imaginary positive current.

Benjamin Franklin discovered electricity and assigned the two kinds of charge the names Positive and Negative in 1750. Earnest Rutherford discovered the structure of the atom in 1911. We have only been confused for a little over 100 years. For the 150 years before Rutherford’s discovery, we were not confused, we were just wrong. Maybe in another hundred years or so, we will stop using the imaginary positive current as the convention in our circuit diagrams.

Design a Circuit

To design a simple electrical circuit, choose a device, look up what it need in terms of voltage and current, and then choose batteries and resistors to give it what it needs to operate. We are going to make the circuit shown above, with the LED in it.

1. Find the data sheet.

A data sheet for a typical LED looks like this one, for the Panasonic LN21RPX 5mm Red LED:

LN21RPX 5mm Red LED data sheet.

LN21RPX 5mm Red LED data sheet.

To get this data sheet I searched Digikey for the part number. You can find the datasheet for most electrical components at the places that sell them, if you know the part number. digikey.com, mouser.com, and newark.com are good places to look. adafruit.com and sparkfun.com have more limited supplies of components, and are geared towards hobbyists, so they may be easier sites to navigate.

Note the Absolute Maximum Ratings in the red oval and red rectangle. If you do not exceed any of the Absolute Maximum Ratings, your part is likely to work properly. Also see the Forward Voltage in the green rectangle. Note the Forward Current, (abbreviated IF ) is 20mA. They suggest that you operate this LED at 20mA current. We will need to pick a resistor value to limit the current to 20mA. If you were to connect the battery directly to the LED without a limiting resistor, the LED would glow, briefly, very brightly, and then it would burn out. 

2. Specify the current and power supply

We want a 20mA current to power the LED, and when it is running, the voltage across it will be 2.2V. There’s only one loop, so there is only one value for the current at all places in the loop. We want 20mA to make the LED light up, and we don’t want to go higher than 25mA so we don’t burn out the LED.

We’re going to use a 4.5V battery because it is close to the 5V that we will get from the Arduino.

3. Calculate the voltage drop you need across the resistor.

We apply Kirchhoff’s Voltage Rule. We already know we will have +4.5V from the battery, and, from the data sheet, we know we will have 2.2V across the LED, because the Forward Voltage (VF) at our target Iof 20mA is 2.2V. 

kirchhoff on LED circuit

Kirchhoff’s Voltage Rule applied to a simple LED drive circuit.

This circuit is here. 

So the voltage across the resistor will be 2.3V if we are putting 20mA through the circuit. That 20mA will make the LED light up with its maximum allowable brightness.

4. Calculate the resistance you need

Use Ohm’s Law to determine the value of the resistor.

Use Ohm's Law to calculate the resistance needed to limit the current to 20mA.

Use Ohm’s Law to calculate the resistance needed to limit the current to 20mA.

5. Find a resistor that is close to what you need.

Do we have a 115Ω resistor? No, of course we don’t. Do we have something close? We don’t want to go too much smaller because we don’t want to burn out the LED. A larger resistance will result in a dimmer light, but if the results are bright enough, we will be happy with the circuit and that is the entire point of making circuits, to get them to do what you want.

150Ω, 200Ω, something around those values will be good. 100Ω would be too low a value, and might damage our LED.

6. Hook it up!

A functioning LED drive circuit.

A functioning LED drive circuit.

As far as the electrons are concerned, which is all that really matters in any ordinary circuit, these two circuits below are the same as the one on the left. The black triangle of the diode symbol points toward the source of negative charge, so current will flow and the LED will light.

Alternative LED drive circuit configurations.

Alternative LED drive circuit configurations.

If you forget to put a resistor in the circuit, or put in a value that is much too small in resistance, the LED will light briefly very brightly, and then go out forever.

If you put in a resistor that is too large in resistance, the LED will be dim, or very dim, or you will not be able to see the glow at all.

If you wish to geek out entirely, measure all three voltages to confirm that Kirchhoff’s Voltage Rule actually applies in practice. Then measure the current in the circuit to see if it is what you expect, given the actual resistor, batteries, and LED you are using. All of the values will be a bit different than what we expect from the design. The components are made of real materials that have real variations, and the battery voltage goes down with use.

Forward to Lesson 3: Production Methods

©Paul Mirel 2015: For educational purposes only, you may freely reproduce this information, provided you cite this page as the source. Commercial uses are prohibited.


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