# Resources

Resistor color codes graphic (PNG) – Learn how to decode the color codes on a 4-band resistor using this chart.

Voltage, current, resistance, and Ohm’s law – This tutorial page from SparkFun contains a lot of information about Ohm’s law and the properties of voltage, current, and resistance.

# Parallel and Series Circuits

I recorded this video for the So That Explains It series at COD. It helps to explain why all of the lights go off in a strand of holiday lights when only one bulb goes bad, using the concepts of series and parallel circuits.

# PhET Ohm’s Law Simulation

See how voltage, resistance, and current are related to each other using the equation *V = IR*.

# PhET Circuit Construction Simulation

Build a circuit using household objects or electronic parts.

# Video Transcript

Hello there! Welcome to lecture 23: electric circuits.

Electric circuits are a ubiquitous part of our daily lives. I’m recording this video using a digital camera, with LED lighting. Both of these objects are plugged into wall outlets that provide voltage to the circuits powering the devices. You are watching this video on a smart phone, tablet, or computer that uses circuitry to function. The smart phone or tablet is powered with a battery, and the computer plugs in to the wall.

Learning the fundamentals of electric circuits allows us to better understand the basics of how all of our electronics works.

Each of the following concepts will be discussed in this video: voltage, resistance, current and Ohm’s law, power, circuits, and alternating and direct current.

## Voltage

Voltage is a property of electric circuits that’s very prevalent in our lives. Voltage has a symbol of the capital letter V. The units for voltage are volts, which also has a symbol of the capital letter V.

Voltage is a measure of electric potential, a property we discussed in lecture 22. Usually, voltage is measured as a difference in electric potential between two points. This is why you may hear the term “potential difference” used in discussions of voltage.

Voltage can be created in different manners. Chemical means can be used to separate positive and negative charges, for example, in a battery. A battery is a source of constant voltage. Double A, triple A, and D-cell batteries are commonly used in household items like flashlights. These output a constant 1.5 volts. A 9-volt battery generates 9 volts of potential difference. Coin cell batteries used in smaller electronics like calculators usually generate either 1.5 volts or 3 volts.

Alternatively, a generator can be used to produce voltage. Power plants generate electricity using a process we’ll discuss in lecture 25. The value of this voltage changes over time. In the United States, our power generation creates a voltage that fluctuates at a frequency of 60 hertz and that has an average voltage of 120 volts in our homes.

## Resistance

Resistance is the property of a material that impedes the flow of electrons throughout that material. It has a symbol of the capital letter R. The units of resistance are ohms, which has a symbol of the capital Greek letter Omega.

The resistance of a material is related to different properties of that material. One of the properties is the resistivity of that material. Resistivity has a symbol of the lowercase Greek letter rho. The units used for resistivity are ohm-meter (an ohm times a meter). For pure substances, resistivity is a property inherent to that material. The smaller the resistivity of a material, the better conductor it is. For example, copper has a resistivity of approximately 1.7 times ten to the negative 8 ohm-meters at room temperature.

Resistance is equal to the resistivity of an object, times its length, divided by its surface area. In other words: R equals rho-L divided by A. We can use this equation to determine the effects of each of these variables on resistance. The larger the resistivity, the larger the resistance. The longer the object, the larger the resistance. However, the larger the cross-sectional area, the smaller the resistance.

This equation is used to create electric circuit elements known as resistors. Resistors are used in electric circuits for many reasons: to create particular voltage and current properties and to amplify certain frequencies of electronic waves, among many other applications. They are frequently used by electrical and electronics engineers, and can be found in nearly all electric circuits.

## Current and Ohm’s law

Current describes the flow of electric charge through a circuit. Current flows in a circuit when there is a complete path including a voltage source. Using a battery, this means there must be a complete path between the plus and minus ends of the battery.

Current has a symbol of the capital letter I. The units used for current are amps, short for amperes. One amp is equal to one coulomb per second. This means that one amp of current is equal to one coulomb of charge moving past a given point every second.

The relationship between current, voltage, and resistance is given by Ohm’s law. Ohm’s law states that v equals I R. In other words, the voltage in a circuit equals the current flowing through the circuit times the resistance of the circuit. Ohm’s law can be used for an entire circuit, or also for particular sections or elements of a circuit. For example, Ohm’s law can be used to calculate the voltage over one particular resistor in a circuit that contains more than one resistor.

Let’s do an example of Ohm’s law. If I have a circuit that includes a voltage source of 9 volts that includes a resistor of 5,000 ohms, how much current flows through the circuit? Use V equals I R. 9 volts equals 5,000 ohms times current. Divide both sides by 5,000 ohms and we see that the current equals 0.0018 amps, also known as 1.8 milliamps.

## Power

Power describes the rate at which energy is consumed in a circuit element. This is the same physical property that we discussed in lecture 7. The symbol is the capital letter P, and the units are watts. The equation for power in an electric circuit is P equals I times V. Power equals current times voltage.

Power can be generated in a circuit (batteries, power supplies, and generators can do this), and also consumed in a circuit (by resistors, lamps, and so on). Power is conserved, which means that all of the power consumed in a circuit is equal to all of the power generated in a circuit.

From a practical perspective, power is consumed by doing useful things in a circuit. An electric stove consumes power and uses it to generate heat to cook food. A lightbulb consumes power and uses it to generate light. The tuning circuits in radios and televisions consume power to allow us to listen to music or watch our favorite TV show. The electronics in your smartphone consume power to operate the device.

Lightbulbs are sold with a power rating in watts. That power rating gives us an idea of how strong the light source is. A higher power rating means more light will be given off by the bulb. Incandescent lightbulbs have power ratings usually between 40 and 100 watts. A 60 watt bulb would be used in a typical light fixture, not too bright, not too dim. LED bulbs have much lower power ratings. These are usually only 6 to 12 watts, but generate equivalent levels of brightness as incandescent bulbs.

While we’ll discuss the physics behind the different types of bulbs in more detail in lecture 30, for now I will simply point out that incandescent bulbs generate lots of heat. The 60 watts the bulb consumes goes to generate some light, but also a lot of heat. An LED bulb is much more efficient. The power it consumes generates mostly light, and only a very small amount of heat. This efficiency is better for the environment, and saves us money on our electric bills.

Speaking of electric bills, if you have ever paid one, you have probably noticed that the units used in the bills are kilowatt-hours. This is a unit of energy. Recall that energy equals power times time. Because kilowatt is a unit of power, and hours are a unit of time, a kilowatt-hour is a unit of energy. One kilowatt-hour is equal to consuming one thousand watts of power during the time period of an entire hour. Our electric bills charge us for the energy we consume every month.

## Circuits

A circuit is a closed path where current flows. Circuits can consist of different circuit elements: voltage sources such as batteries, resistors, lightbulbs, motors, and so on. Some circuits have only a few elements. Some circuits have many elements and are much more complicated. All circuits can be analyzed using Ohm’s law, conservation of energy, and conservation of charge. Electrical engineers take classes in circuit analysis to learn how to design circuits with specific properties.

For example, a simple circuit can consist of a battery, a resistor, and a wire to connect them in a closed path. We can use Ohm’s law to calculate the value of the current flowing through the resistor. We can use the power equation to determine how much power is consumed by the resistor and created by the battery.

As far as we need to know in this class, while there are many different types of circuits, the two primary configurations of circuit elements are series and parallel. Let’s consider a circuit with multiple resistors now, instead of one.

The resistors, in this example there are three, can be connected in series. In a series circuit, all circuit elements are connected in the same loop. Due to conservation of charge, every resistor will experience the same amount of current flow. Because electrons are forced to travel through all of the resistors in order to complete their path from one end of the battery to the other, the total resistance in a series circuit is greater than the resistance of any of the individual resistors. In series, the total resistance of the circuit is equal to the sum of the individual resistors.

Because there is only one path for current to flow, when two or more circuit elements are connected in series, if one of them becomes broken or disconnected and disrupts the flow of current, the other circuit elements will also become disconnected. This can be demonstrated in a series circuit of two lightbulbs. If one of the lightbulbs is disconnected, both lights will turn off. Many cheap holiday lights are like this. If one of the bulbs breaks, the rest of the bulbs turn off as well. I can simulate this in a strand of holiday lights by taking one of the bulbs out. This turns off all of the other bulbs in the strand of lights.

Due to conservation of energy, the voltage experienced by each resistor in a series circuit will be smaller than the voltage of the battery. If two series resistors have the same value, then the voltage drop over each resistor will be one half the battery voltage. If three series resistors have the same value, the voltage drop over each one will be one third the battery voltage. If we build a circuit, we can use a multimeter to measure this voltage. We can determine how much power is consumed by each resistor in a series circuit by using a combination of Ohm’s law and the power equation. We know the current flowing through the circuit from Ohm’s law and taking the sum of both resistances. We find that the power consumed by an individual resistor in a series circuit equals I-squared R. That is, current squared times the resistance of the individual resistor.

Resistors can also be connected in parallel. That is, each resistor is connected in its own loop, but are connected end to end, hence the name parallel. Due to conservation of energy, each resistor will experience the same amount of voltage, which in this case is equal to the voltage of the battery. Because electrons have multiple different paths to follow, the total resistance in a parallel circuit is less than the resistance of any of the individual resistors.

Because there are now multiple paths for current to flow, when two or more circuit elements are connected in parallel, if one of them becomes broken or disconnected, the other circuit elements will continue to function normally. This can be demonstrated in a parallel circuit of two lightbulbs. If one of the lightbulbs is disconnected, the other light remains unaffected. Current can still flow through that path. Our homes are wired in parallel. If I turn off the kitchen light, my refrigerator is still able to continue working.

Due to conservation of charge, the current flowing through each resistor in a parallel circuit will be smaller than the current flowing through the battery. If two parallel resistors have the same value, then the current flowing through each resistor will be one half the current flow through the battery. If three parallel resistors have the same value, then the current flowing through each resistor will be one third of the current flow through the battery. If we build a circuit, we can use a multimeter to measure this current. We can determine how much power is consumed by each resistor in a parallel circuit by using a combination of Ohm’s law and the power equation. Due to conservation of energy, we know that the voltage over each resistor is equal to the battery voltage. We find that the power consumed by an individual resistor in a parallel circuit equals V-squared over R. That is, voltage squared divided by the resistance of the individual resistor.

Two other types of circuits are open circuits and short circuits.

In an open circuit, there is no complete path for current to flow. Electrons do not move, and none of the circuit components operate. A switch can cause an open circuit. Sometimes this is useful, for example when we want to turn the lights off in our bedrooms to go to sleep at night. A switch opens the circuit and prevents current from flowing through the lights.

A short circuit is a circuit with a very low resistance path that electrons can take. Electrons will proportionally travel through the path of least resistance. If there is a path of zero resistance, such as with a wire, then all current will flow through that path. Because resistance is very low, current will become extremely high. If current becomes very high, so will power. This will cause a lot of heating, and eventually, wires and other circuit components can melt. Short circuits can be very dangerous, and electrical engineers learn how to spot short circuits and avoid them when building circuits.

In this demo, I use a switch to cause a short circuit, creating a low-resistance path that bypasses the lightbulb. When I close the switch, current flows through the switch instead of through the lightbulb, causing the bulb to turn off. I can’t keep the switch closed for too long. It will drain the battery, and heat up, possibly melting if left in this condition for too long.

## Alternating and direct current

The voltage and current in a circuit can exhibit one of two different properties. One possibility is that the voltage and current stay constant over time. This is known as direct current or DC. In a DC circuit, our measurements of voltage and current will stay the same.

Batteries are capable of producing a DC voltage. Double A batteries generate a constant 1.5 volts. Most consumer electronics require DC to either function or to charge their batteries. Most of these devices contain a converter that generates the correct DC voltage to carry this out.

On the other hand, it is possible for voltage and current signals to change over time. Usually they will oscillate in a sinusoidal pattern, like a wave. This is known as alternating current or AC. A device known as an oscilloscope can be used to record how voltage changes and creates a graph of voltage plotted with respect to time.

For reasons we’ll discuss in lecture 25, power plants generate alternating current. When we plug something in to a wall outlet, that device is powered with AC. The frequency of the voltage oscillation is 60 Hz in the United States, and the average value of the voltage is 120 volts in this country. When traveling to other countries, it is important to bring an adapter to ensure that our electronic devices continue to function when plugged in to different values or frequencies of voltage.

A diode is a circuit element that acts like a one-way valve. A diode only allows current to flow through in one direction. When connected in a DC circuit, a diode can prevent current from flowing if it is connected backwards. A light-emitting diode, LED, is a diode that also emits light. When connected into a circuit in the forward direction, current flows through and the LED lights up. When connected backwards, current is blocked and the LED remains off.

In an AC circuit, a diode allows current to flow in only one direction. It transmits through the positive current and blocks the negative current. We can see this effect as the LED only lights up when it allows current to flow through, every half cycle.

A circuit built with a regular, non-light-emitting diode can be used to show the difference between the input and output voltages on an oscilloscope. The input signal is yellow, and the output signal, after negative voltages have been blocked, is shown in purple. This circuit is called a rectifier. A rectifier is a circuit that only allows current to flow in one direction.

Because every half cycle, the diode blocks current, this would not be an efficient circuit to convert AC to DC. For that we can use a circuit called a full-wave rectifier. The configuration of diodes in this circuit causes current to always flow through in one direction. The output wave on the oscilloscope shows that current flows through during both cycles of the AC wave, and all of the voltage is positive.

To smooth out the oscillations in this output voltage and to obtain a nice, smooth, DC voltage, we use a device called a capacitor. A capacitor smooths out changes in voltage in a circuit. This forms the basis of the converters used to charge DC-powered electronics that obtain power from a wall outlet.

Thanks for taking the time to learn about electric circuits! Until next time, stay well.