# How To Build And Analyze Your First DC Circuit

## A First Circuit

In my last Hub, I gave some ideas on how to set up a beginner electronics workspace. In this Hub, we'll learn some basic principles about a certain class of electronic circuits known as Direct Current (DC) circuits and build and analyze a simple DC circuit. I encourage you to follow along with your own circuit!

## Two Types Of Current

First, a little theory. There are two basic types of current. But what is current? (If you already know this, go ahead and skip ahead.) Current is the flow of charged particles. There are two possible polarities for charged particles: negative and positive. Electrons, which you've probably heard of, are negatively charged particles. These are the most commonly found charged particles actually flowing through the wires, resistors, and other components of electronic circuits.

However, there is a very common convention in electronics to use a "conventional" current that is a hypothetical positive charged particle flowing in the opposite direction. Though there may not actually be a positively charged charge carrier flowing through a wire, if there *is* a negatively charged charge carrier, like an electron, flowing in one direction, say, from A to B, that is equivalent to if there were a positively charged charge carrier flowing in the opposite direction from B to A.

Take home message: most electronic circuit analysis considers *current*, unless specifically stated otherwise, to be a flow of positive charge carriers.

Now, the two different types of current are not the polarities of the charge carriers I was just talking about. The two different types of current differ in the way that the charge carriers flow. In **Direct Current** (**DC**), the charge carriers flow forward and onward always in the same direction, whereas in **Alternating Current** (**AC**), the charge carriers flow in one direction for a little while, then go back in the opposite direction for a little while, and so on.

Batteries are sources of DC electricity, while the electricity in your home's wall outlet is of the AC variety. Since we'll be using batteries in the circuit to come, it will be a DC circuit.

## Voltage and Resistance

I've briefly mentioned above the concept of current as a flow rate of charge carriers. Now I'd like to talk about two more concepts frequently encountered in electronics: voltage and resistance.

If current can be compared to the flow of water through a pipe, voltage could be considered the pressure that is behind that flow. Voltage is also sometimes referred to as electromotive force, or EMF. There is no such thing as a voltage at a single point without reference to any other point; a voltage is always a potential difference between two points.

The concept of resistance should be clear by its name. It is that property of the conducting medium, be it a wire, resistor, or other component, that prevents the unlimited flow of current through it. A tube filled with rocks has a higher resistance to the flow of water through it than an empty tube, and some metals, like copper, have much lower resistance to electrical current flow than other metals. A material through which current can flow with low resistance is called a conductor, while a material through which current cannot flow (which has high resistance) is called an insulator.

Voltage is measured in units of volts (V), resistances are measured in units of ohms (Ω, the Greek letter Omega), and current is measured in units of amperes (A), though at the hobbyist scale, you're more likely to encounter amperages at the milliampere (mA), or thousandths of an amp level.

## A Very Simple DC Circuit

Shown at the right is one of the simplest possible DC circuits, consisting of only a single battery and a single resistor. This is known as a schematic drawing, which uses symbols to represent actual components. The symbol next to the V is the symbol for a battery, and the symbol next to the R is the symbol for a resistor. The connecting lines represent wires or any general conductor connecting the components in the schematic drawing. The little black triangle next to the I does not represent any component, but simply denotes the direction of the current flow through the circuit. Some schematic drawing standards place an arrow adjacent to the conductors in the circuit to identify the current flow.

## Implementing The Circuit

Let's build the circuit shown in the schematic above. For the battery, I've used a 1.5 V AA battery like you can find at any grocery store, and for the resistor, I've used a 1,200 Ω or 1.2 kΩ (the 'k' or *kilo* prefix means to multiply the figure by 1,000) resistor. Shown below is the circuit wired using a breadboard. Each of the columns A-E of a given row are electrically connected.

## Analysis

Let's go back and consider the schematic, with the real-world implementation in mind. The battery used has a voltage of 1.5 V, so that is the value for V in the schematic. The resistor has a resistance of 1.2 kΩ, so that is the value for R in the schematic. We can figure out what the resulting current I through the circuit is using the relation known as **Ohm's Law**. Ohm's law states that if you know the values of two of voltage, current, or resistance, you can find the value of the third by using the desired one of the following equations: V = IR, I = V/R, R = V/I.

## Ohm's Law

The picture to the right shows this graphically. Cover up the unknown value and its calculation method using the other two is shown. For example, if voltage is unknown, cover the V. I and R are beside each other, so multiply them together to get V. If I is unknown, cover it. V is over R, so divide V by R to get I. And if R is unknown, covering it shows that to get it, you divide V by I.

Let's use Ohm's Law to figure out the expected value of I, the current flowing through the resistor. The resistor is connected to the terminals of the battery, so the voltage across the resistor is the same as the voltage of the battery, so the value for V is 1.5 V. And we stated earlier that we were using a 1.2 kΩ resistor, so the value for R is 1,200 Ω. Using Ohm's law, the expected value for I given these values for V and R is 1.5 / 1,200 or about 0.00125 A or, rounding, about 1.3 mA.

## Measurement

We can test our calculations by actually measuring the true resistance of, the voltage across, and the current through the resistor in our implementation of the circuit. First, let's measure the true resistance of the resistor in the circuit.

To measure the resistance of a resistor in a circuit, you first want to remove any voltage sources like batteries from the circuit so that there is no current flowing through the resistor to be measured. Next, set your multimeter to the appropriate resistance range, if it doesn't automatically scale. For instance, I expect the resistance of the resistor I'm going to measure to be about 1.2 kΩ, and my multimeter has ranges of 200 Ω, 2,000 Ω, 20 kΩ, and more. If I set it to 200 Ω, that would be too low, and if I set it to 20 kΩ, that would be too high, so I set it to 2,000 Ω. Having removed my battery and set my multimeter to the right setting, I get the following resistance measurement for my resistor:

So the measured value for this 1,200 Ω resistor is 1,178 Ω. That's within the plus-or-minus five percent stated tolerance for this resistor.

Next, we can measure the voltage across the resistor when the battery is connected by switching the multimeter to voltage measurement mode in the 2000 mV range (2000 mV, or 2 V, is the closest range to our expected 1.5 V reading) and reinserting the battery. The measured voltage is seen below.

To measure the current I through the circuit, we need to modify the circuit in that we need to place the multimeter in current measurement mode in series between the battery and the resistor, as shown in the schematic at the right. The circle with the A and the arrow through it is the schematic symbol for a current measuring device, also called an ammeter. Shown below is the multimeter placed in series with the resistor by lifting the battery terminal wire and placing the leads of the multimeter on the battery terminal wire and the top lead of the resistor.

The closest range scale to our expected 1.3 mA is the 2,000 μA scale. The 'μ' symbol is the Greek mu symbol, which is the prefix indicating one millionth. Two thousand millionths of an amp is equivalent to two milliamps (remember, milli is the thousandths prefix). The measurement indicates that the measured current is approximately 1.1 mA, which is pretty close to the expected value of 1.3 mA (which calculated value was based on the nominal voltage and resistance values of the battery and resistor).

If we try to apply Ohm's Law to our measured values, for instance, to see if our measured voltage (1.389 V) and resistance (1,178 Ω) divide to give our measured current value, we notice that the calculated value of 1.389 / 1,178 equals approximately 1.18 mA, which is indeed very close to our measured current of 1.1 mA. Part of the small discrepancy is rounding error and using more significant figures than we may be entitled to use, and part is because the multimeter, while measuring voltage and current, can change very slightly the voltage across and current through the resistor (i.e., the actual value would be slightly different if it were not being measured).

I hope you learned something from this Hub! In the next one, I'll talk about simple DC circuits with multiple resistors connected in series. Thanks for reading!

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