Circuit Analysis: Crash Course Physics #30

Summary

This script from Crash Course Physics dives into the world of circuit analysis, using the festive theme of holiday lights to explain electrical concepts. It covers the basics of DC circuits with resistors in series and parallel, employing Ohm's Law to calculate current, voltage drops, and resistance. The lesson demonstrates how to simplify complex circuits to a single equivalent resistance and then expand back to determine individual current and voltage values. Practical applications include using voltmeters and ammeters to measure these values, ensuring a hands-on understanding of electrical principles.

Takeaways

• 🌟 Physics is everywhere, even in holiday lights, which can be analyzed using circuit analysis.
• 🔌 Ohm's Law is fundamental in electrical circuits, relating voltage, resistance, and current, and can be used to solve for unknown variables.
• 🔍 Circuit analysis involves breaking down a circuit into its components to understand the system as a whole.
• 🔗 In series circuits, resistors are connected end-to-end, sharing the same current, and their resistances can be summed up.
• 🔄 In parallel circuits, resistors are connected across the same voltage, with the total resistance being less than any individual resistor.
• 📚 The equivalent resistance simplifies complex circuits to a single resistor, making it easier to calculate the overall current.
• ⚡ The current in a circuit can be determined by knowing the voltage and the total equivalent resistance.
• 🔌 After calculating the total current, you can determine the voltage drop and current through each individual resistor.
• 🔧 Practical tools like voltmeters and ammeters are used to measure voltage and current in real circuits, ensuring the theoretical calculations are accurate.
• 🔬 Understanding circuit analysis not only helps with academic knowledge but also with practical applications, such as setting up holiday light displays.
• 🎓 The script provides a step-by-step guide on how to analyze and measure various aspects of a DC circuit with resistors in series and parallel.

Q & A

What is the main topic discussed in the script?

The main topic discussed in the script is circuit analysis, specifically in the context of understanding how electricity works in holiday light displays and using Ohm's Law to calculate various electrical properties in a circuit.

What are the three key components of every electrical circuit mentioned in the script?

The three key components of every electrical circuit mentioned are voltage, resistance, and current.

How is Ohm's Law defined in the script?

Ohm's Law is defined in the script as the relationship between voltage, resistance, and current, where if you know two out of the three variables, you can solve for the remaining one.

What is the process of simplifying a complex circuit to a single equivalent resistor?

The process involves combining resistors in series by adding their resistances together and using a formula for resistors in parallel to find an equivalent resistance that is smaller than any of the individual resistors.

How is the equivalent resistance of resistors in parallel calculated?

The equivalent resistance of resistors in parallel is calculated using a formula that results in a single resistor with an equivalent resistance smaller than any of the individual resistors in the branches.

What is the example circuit configuration given in the script?

The example circuit configuration includes a 20-volt battery, a 10-Ohm resistor, a parallel formation of more resistors with one branch having two resistors in series (15 Ohms and 2 Ohms), another branch with a 6 Ohm resistor, and another parallel formation of resistors (3 Ohms and 5 Ohms each).

How is the current in the circuit calculated after simplifying the resistors?

The current in the circuit is calculated using Ohm's Law, where the current is found by dividing the voltage of the power source by the total equivalent resistance of the circuit.

What are the two devices used to measure voltage and current in a real circuit?

The two devices used to measure voltage and current in a real circuit are a voltmeter and an ammeter, respectively.

Why is it important to have a high resistance for a voltmeter when measuring voltage in a circuit?

A high resistance for a voltmeter is important to avoid altering the actual circuit, ensuring that the same voltage is read across both the voltmeter and the device being measured with minimal current flowing through the voltmeter.

Why should an ammeter have near-zero resistance when measuring current in a circuit?

An ammeter should have near-zero resistance to avoid changing the current in the circuit. It measures the current in Amperes by connecting in series with the circuit without significantly affecting the circuit's operation.

What is the significance of the conservation of charge principle in the context of the script?

The conservation of charge principle is significant in the script as it ensures that the sum of the currents entering and leaving a junction in a circuit is equal, which is used to verify the correctness of the calculations for the current through different branches of the circuit.

Outlines

00:00

💡 Understanding Holiday Lights Through Physics

This paragraph introduces the concept of circuit analysis in the context of holiday lights, emphasizing the importance of understanding electrical components like voltage, resistance, and current. It explains how Ohm's Law connects these properties, allowing one to calculate the unknown variable if two are known. The paragraph uses the example of a holiday light circuit to demonstrate how to find the equivalent resistance and the resulting current. It also highlights the educational value of applying physics to everyday situations like holiday lighting.

05:00

🔌 Circuit Analysis and Ohm's Law in Action

The second paragraph delves deeper into circuit analysis, focusing on calculating the equivalent resistance of resistors in series and parallel. It provides a step-by-step example of how to simplify a complex circuit with various resistors to a single equivalent resistance and then use Ohm's Law to determine the current in the circuit. The paragraph also explains how to expand the simplified circuit back to its original form to find the current and voltage drop across each individual resistor, reinforcing the practical application of Ohm's Law.

10:06

🔍 Measuring Voltage and Current with Instruments

The final paragraph discusses the practical aspect of measuring voltage and current in a circuit using a voltmeter and an ammeter, respectively. It explains the importance of connecting these instruments correctly to avoid altering the circuit's behavior. The paragraph provides tips on using these devices without causing damage or inaccurate readings, emphasizing the hands-on approach to verifying the calculations made using Ohm's Law. It concludes with a brief mention of the production team behind the educational video and encourages viewers to explore related content from PBS Digital Studios.

Keywords

💡Physics

Physics is the natural science that studies matter, its motion, and behavior through space and time, and the related entities of energy and force. In the video, physics is the foundational knowledge that allows the viewer to understand and analyze electrical circuits, particularly how holiday lights work, showcasing its omnipresence and practical applications in everyday life.

💡Circuit Analysis

Circuit analysis is the process of understanding how electricity works within a circuit by breaking it down into its key components. The script emphasizes the importance of circuit analysis in determining the current required to power holiday lights, illustrating how it can be used to study and solve complex electrical systems.

💡Ohm's Law

Ohm's Law is a fundamental principle in electrical engineering that relates voltage (V), current (I), and resistance (R) in a circuit through the formula V = IR. The video uses Ohm's Law to explain how knowing any two of these variables allows for the calculation of the third, which is crucial for understanding the operation of a circuit with holiday lights.

💡Resistor

A resistor is a passive component in an electrical circuit that opposes the flow of current. The script discusses how resistors, in various configurations like series and parallel, are used to control the current and voltage in holiday light displays, highlighting their role in circuit design.

💡Voltage

Voltage, or electric potential difference, is the force that pushes electric charge through a conductor. In the context of the video, voltage is the driving force behind the current in holiday light circuits, and understanding it is key to calculating the required current and the behavior of the circuit.

💡Current

Current is the flow of electric charge in a circuit, measured in amperes. The script uses the concept of current to explain how the total current in a holiday light circuit can be determined and then distributed across various components, such as individual light bulbs.

💡Series and Parallel Formations

Series and parallel formations refer to the way resistors or other components are connected in a circuit. In series, components share the same current, while in parallel, they share the same voltage drop. The video script uses these concepts to demonstrate how to calculate the equivalent resistance of a complex circuit and to understand the distribution of current and voltage.

💡Equivalent Resistance

Equivalent resistance is the total resistance of a circuit or a part of a circuit that can be substituted for the actual components without changing the circuit's behavior. The script explains how to calculate the equivalent resistance of resistors in series and parallel, which simplifies the analysis of complex circuits like holiday light displays.

💡Voltmeter

A voltmeter is a device used to measure the voltage difference between two points in a circuit. The video mentions the use of a voltmeter to confirm the theoretical calculations of voltage drops across various components in a holiday light circuit, emphasizing the practical application of measuring tools in circuit analysis.

💡Ammeter

An ammeter is an instrument that measures the electric current flowing through a circuit. In the script, the ammeter is described as a tool to measure the current in a circuit without altering its flow, which is essential for verifying the calculations made during circuit analysis.

Highlights

Studying physics allows one to see its principles everywhere, including in holiday lights.

Circuit analysis is a method to understand electricity in complex systems like holiday light displays.

Ohm’s law relates voltage, resistance, and current, allowing calculation of one if the other two are known.

Resistors in series are combined by adding their resistances, simplifying the circuit.

Resistors in parallel are combined using a formula that results in an equivalent resistance smaller than the smallest individual resistor.

An example circuit with a 20-volt battery and various resistors in series and parallel is used to demonstrate analysis.

Equivalent resistance simplifies complex circuits to a single resistor for current calculation.

Once current is known, further analysis can determine voltage drops and currents through individual resistors.

Conservation of charge is demonstrated as the sum of branch currents equals the total current entering the junction.

Voltage drop across resistors in series is proportional to their resistance, with larger resistors dropping more voltage.

A voltmeter is used to measure voltage without altering the circuit, with high resistance to avoid current draw.

An ammeter measures current in series with the circuit, with near-zero resistance to avoid affecting the circuit.

Misusing voltmeters and ammeters can damage the device or fail to measure correctly due to their resistance characteristics.

Circuit analysis enables understanding and practical application of Ohm’s Law in real-world scenarios like holiday lighting.

The video demonstrates the practical use of circuit analysis in calculating and measuring electrical properties in DC circuits.

Crash Course Physics is produced in collaboration with PBS Digital Studios, offering a variety of educational content.

Transcripts

When you study physics, you can start to see it everywhere – even here.

As an engineer who studied physics, I have to say one the most interesting parts of the holidays is the lights.

Just think of all of the crazy displays that you see, and what it would take to figure out the current required to power all of the tiny light bulbs that make them glow.

So many resistors.

Now, I’m not going to ask you to diagram the holiday lights on your neighbor’s house.

But, one of the best ways to understand how electricity works in a system like that, is through circuit analysis:

the process of breaking down a circuit into its key components, and studying each one, to see what it can tell you about the others.

So far, you’ve learned about the key components of every electrical circuit – namely voltage, resistance, and current.

These properties are all related to one another through Ohm’s law.

This means that if you know two out of the three variables, you can solve for the remaining one.

For example, you can take a bunch of resistors in a circuit, find their equivalent resistance, and then use the voltage to figure out what the current is.

And when you know the current, you can get even more important information, like the voltage across a particular component, or the current through a specific wire.

So if nothing else, today’s lesson in circuit analysis will help you appreciate holiday lights on a whole new level.

[Theme Music]

Let’s keep things simple.

There’s an enormous number of circuit-building methods that I’d love to go over with you, but we’re going to stick to the basics, which you’ll use in every circuit problem you’ll encounter.

These are DC circuits, with resistors in series and parallel formations.

You’ll recall that series formations occur when resistors are connected along the same path, so they have the same current passing through each one.

And parallel connections are when resistors are placed on wires that branch out from a single point, all having the same voltage drop across them.

And to find the equivalent resistance of resistors in series, you just add their resistances together.

For resistors in parallel, meanwhile, you use a different method – one that gives you a resistor with an equivalent resistance that’s smaller than any of the individual resistors in the branches.

Now, let’s put these equations to work!

Here’s an example of a circuit with resistors in both series and parallel formations.

Say you have a 20-volt battery, immediately followed by a resistor of 10 Ohms.

Following that, there’s a parallel formation of more resistors:

One branch consists of two resistors in series, one of 15 Ohms and one of 2 Ohms.

The other branch has a 6 Ohm resistor, and then another parallel formation of resistors, 3 and 5 Ohms each.

Our goal is to simplify everything down to one resistor, which will have the equivalent resistance of all of these resistors combined.

With that equivalent resistance, you can then know what the resulting current is in the circuit.

Then, using Ohm’s Law, you can calculate the voltage across, and current through, each resistor.

OK, let’s do the easiest steps first.

Start by finding the resistors in a series.

You can collapse these down into a single resistor by simply adding their resistances together.

In this case, you add the 15 and 2 Ohm resistors into a single, 17 Ohm equivalent resistor.

Now that branch contains a single resistor.

Let’s look at the other branch.

This one has a single resistor and then two in parallel.

So let’s start by turning the parallel connection of the 3 Ohm and 5 Ohm resistors into one equivalent resistor.

Using our equation for resistors in parallel, you find that they simplify to a single resistor of about 1.88 Ohms.

Then, you can add the newly formed resistor to the 6 Ohm one, and the branch simplifies even more – to a single resistor of 7.88 Ohms.

All right, you’re almost there!

Now, let’s combine the 17 Ohm and 7.88 Ohm resistors, which are in parallel, into one resistor and its resistance turns out to be 5.38 Ohms.

And with that, you’re left with only two resistors in series, which you can combine to form a single resistor with the equivalent resistance of 15.38 Ohms.

Now, there’s only one resistor left, which means you can easily find the current drawn from the battery!

Using Ohm’s Law, you can find that the current through a circuit with a 20 volt battery and an equivalent resistance of 15.38 Ohms is about 1.30 Amperes.

Just pause for a moment and appreciate what you’ve done so far.

You were able to take what you knew about the power source and the number and configuration of the resistors to figure out the current that runs through the circuit.

And it wasn’t that hard, was it?

And now that you’ve determined the current, you can learn so much more!

With the total current in the system, you can expand the equivalent circuit back to its original form.

And while you’re doing that, you can determine both the current through, and the voltage drop across, every single resistor.

Just go back one step to the ten Ohm resistor, and the 5.38 Ohm resistor.

Nothing has changed about the current through the circuit.

And the two resistors are in series, so the current flowing through them is the same.

But the voltage drop across each resistor is different.

You can calculate the voltage drop across each resistor by using Ohm’s Law, V equals I times R.

You know the current, I, and you know each resistance, R, so you simply use them to find the distinct voltage drop, V, across each resistor.

The voltage drop across the 10 Ohm resistor turns out to be 13 Volts, which leaves the remaining voltage drop across the rest of the circuit to be 7 Volts.

And you don’t have to do anything with the 10 Ohm resistor, since that’s not a combination of resistors.

So the current through and voltage across that circuit element doesn’t change.

In order to complete the rest of the circuit, let’s expand the 5.38 Ohm resistor back out again, to those two resistors in parallel.

Now, you know that any two resistors in parallel have the same voltage drop, so both the 17 Ohm resistor and the 7.88 Ohm resistor have a voltage drop of 7 Volts, just when they were collapsed into one.

But the current through each branch is not the same.

Since you know the resistance of, and voltage across, each resistor, you just use Ohm’s Law again to calculate the current through each wire.

The 17 Ohm resistor, with a voltage drop of 7 Volts, will have a current of 0.41 Amperes.

And the 7.88 Ohm resistor, with the same voltage drop of 7 Volts, will have a current of 0.89 Amperes.

And look at this: If you add these two currents together, they equal the 1.3 amperes.

That’s the same value for the current that enters the junction where the wires split.

This must be true, to satisfy conservation of charge, because remember: What goes in must come out!

Now, let’s expand the resistor on the right into its two components, a 6 Ohm and a 1.88 Ohm resistor.

The current through these two is still 0.89 Amperes, but the voltage drop of 7 Volts is now split across the two resistors.

All you have to do is implement Ohm’s law yet again, multiplying current and resistance in order to find the voltage drop.

So 0.89 Amperes times 6 Ohms equals a 5.33 Volt drop.

And 0.89 Amperes times 1.88 Ohms equals the remaining 1.67 Volt drop.

Now, It’s good to check that you’re on the right track by looking at the relationships of all of these values.

Keep in mind that, for resistors in series, the larger the resistance is, the larger the voltage drop that’s required.

Think of a big light bulb and a tiny light bulb on the same wire of holiday lights, using the same current.

The little light bulb doesn’t draw nearly as much power, so it uses less voltage for the same amount of current passing through it.

OK, back to work!

Our 1.88 Ohm resistor is a combination of a 3 Ohm and 5 Ohm pair of resistors in parallel.

So the voltage drop across each resistor is still 1.67 Volts, but the current passing through each will be different.

Using Ohm’s Law, you can divide the voltage across each resistor by its respective resistance, giving you the current through each branch.

1.67 volts divided by 3 Ohms gives you a current of 0.56 Amperes through the 3 Ohm resistor.

And 1.67 volts divided by 5 Ohms gives you a current of 0.33 Amperes.

And since 0.56 plus 0.33 Amperes equals the 0.89 Amperes that enters the wire at the split, you know you’re on the right track.

One last step!

The 17 Ohm resistor is a series combination of a 15 Ohm and 2 Ohm resistor.

Here, the current through them – 0.41 Amperes – stays the same, while the voltage drop across each one can be found using Ohm’s Law.

0.41 Amperes times 15 Ohms equals 6.17 volts across the 15 Ohm resistor.

And 0.41 Amperes times 2 Ohms equals the remaining 0.82 Volts across the 2 Ohm resistor.

To check your work, you can go back and see that the two voltage drops equal the total voltage drop across each branch after the 10 Ohm resistor.

And you’ve done it! Congrats!

You’ve taken a whole circuit, simplified it down to the bare minimum, then expanded it again, discovering the current and voltage values for every single resistor.

But, even though we all love math, what if that’s not enough for you?

What if you physically constructed this circuit yourself, and you wanted to measure the values so that you knew your math checked out?

To measure voltage, you’d just need a tool known as a voltmeter.

Pretty creative, I know.

Now, you want a way to measure voltage without altering the actual circuit.

No solution is perfect, but you can get a pretty accurate reading by attaching the voltmeter on either side of the device that you want to measure.

And you do it that way, because you know that any components connected in parallel will have the same voltage.

But even if you measure the voltage, you still want to avoid changing the resulting circuit.

So, what you do is give the voltmeter a resistance that's so high that it’s considered infinite, relative to the rest of the circuit.

With an “infinite” resistance, the same voltage is read across both the voltmeter and the device you’re measuring, and a tiny amount of current ends up running through the voltmeter.

OK, you’re a stickler, and even though you’ve confirmed your voltage, you want to do the same thing with the current.

This time, you’ll use the fact that devices connected in series share the same current.

So, you need a device that can measure current, in series with another component, without changing the current.

This is known as an ammeter, and it measures the current in Amperes by connecting in series with the circuit.

It doesn’t affect the circuit, because the device has a near-zero resistance.

But here’s a pro tip: When you use these devices in the lab, be very careful not to mix up the methods of connection!

Attaching the ammeter, a device with near-zero resistance, in parallel with another resistor, will cause nearly all the current to run through the ammeter, possibly damaging it.

And if a voltmeter is attached in series, you’re not going to see any current flowing, because the resistance is so large!

But used correctly, these devices can not only allow you to confirm your maths, they can also give you a hands-on way to measure the basic principles of Ohm’s Law in action.

And they just might help you raise your holiday-lighting game to a whole new level.

Today, we saw how circuit analysis can be used on any series and parallel configuration of resistors in a DC circuit.

We used Ohm’s Law to go from an equivalent circuit to solving for every current value and voltage drop in the system.

Finally, we saw how to measure voltage and current in a real circuit using voltmeters and ammeters.

Crash Course Physics is produced in association with PBS Digital Studios.

You can head over to their channel to check out a playlist of the latest episodes from shows like PBS Space Time, The Good Stuff, and Indie Alaska.

This episode of Crash Course was filmed in the Doctor Cheryl C. Kinney Crash Course Studio

with the help of these amazing people and our equally amazing graphics team, is Thought Cafe.