Cells, EMF, terminal voltage & internal resistance | Electric current | Physics | Khan Academy

Summary

The video script delves into the concepts of Electromotive Force (EMF), terminal voltage, and internal resistance within a cell, aiming to clarify the distinctions and relationships between these electrical terms. It begins with a practical scenario of connecting bulbs to a battery and observing the dimming effect as more bulbs are added, illustrating the impact of increased current draw on voltage. The script then defines EMF as the energy transferred per coulomb by the battery, typically indicated on the battery itself. However, due to internal resistance within the battery, not all of this energy is gained by the charge as some is lost as heat. This heat loss, dependent on the current and internal resistance, results in a lower terminal voltage—the actual energy per coulomb available at the battery's terminals. The script further explains that as current increases (or the charge moves faster), more heat is generated, leading to a greater drop in terminal voltage. Conversely, at zero current, there is no heat loss and the terminal voltage equals the EMF. Finally, the script presents the equation connecting these variables: Terminal Voltage (VT) equals EMF minus the product of current (I) and internal resistance (R), encapsulating the essence of how these factors interact within a battery.

Takeaways

• 🔋 **EMF Defined**: Electromotive force (EMF) is the energy transferred per coulomb by the battery, often indicated on the battery itself (e.g., 1.5V or 9V).
• 🚫 **EMF vs. Force**: Despite its name, EMF is not a force but a measure of energy.
• 🔌 **Terminal Voltage**: Terminal voltage is the actual voltage or energy gained by a coulomb as it travels from the negative to the positive terminal of the battery.
• ⚡ **Internal Resistance**: The internal resistance of a battery is the resistance encountered by the charge as it moves through the battery's chemicals, which can cause energy loss as heat.
• 💡 **Effect of Current**: As more bulbs (or loads) are connected in parallel, more current is drawn from the battery, leading to a drop in terminal voltage due to increased heat loss from internal resistance.
• 🌡️ **Heat Generation**: The movement of charge through the battery's medium generates heat, which is a form of energy loss that reduces the terminal voltage from the EMF.
• 🚀 **Speed and Heat**: Faster movement of charge through the battery's medium results in more heat generation and thus a greater energy loss, lowering the terminal voltage.
• 🔥 **Current and Heat Loss**: The greater the current drawn from the battery, the more heat is lost due to internal resistance, resulting in a lower terminal voltage.
• 🔁 **Charge Speed and Voltage**: If the charge moves very slowly through the battery, less heat is lost, and the terminal voltage approaches the EMF.
• ⏹️ **Zero Current**: At zero current, there is no heat loss, and the terminal voltage equals the EMF.
• 📐 **Ohm's Law Application**: The voltage drop across the battery's internal resistance (due to current flow) can be calculated using Ohm's law (V = I * R), which helps to determine the terminal voltage.

Q & A

What happens when you connect more bulbs in parallel to a battery?

As more bulbs are connected in parallel, the overall current drawn from the battery increases, leading to a decrease in the brightness of the bulbs due to the higher current demand and the internal resistance of the battery.

What is the Electromotive Force (EMF) of a battery?

The EMF, often indicated on the battery, is a measure of the energy transferred by the battery per coulomb of charge. It is not a force but an energy term, typically expressed in volts (e.g., 1.5V or 9V).

How does the internal resistance of a battery affect the terminal voltage?

The internal resistance of a battery causes some of the energy transferred to the charge to be lost as heat. This results in the terminal voltage being less than the EMF, especially when higher currents are drawn from the battery.

Why does the voltage across a battery drop when more current is drawn?

The voltage drop occurs because as more current flows through the battery's internal resistance, more energy is lost as heat. This heat loss reduces the net energy available to the external circuit, hence the terminal voltage decreases.

What is the relationship between the speed at which charge moves through a battery and the terminal voltage?

The faster the charge moves through the battery, the more heat is generated due to the internal resistance, leading to a greater energy loss and thus a lower terminal voltage.

How does the brightness of bulbs connected to an inverter change when more bulbs are turned on?

As more bulbs are turned on and connected to an inverter, the current drawn from the inverter increases, causing a drop in voltage and a decrease in brightness due to the internal resistance and heat loss.

What is the significance of the term 'internal resistance' in the context of a battery?

The internal resistance is the opposition to the flow of electric current inside the battery. It is significant because it determines the amount of energy lost as heat when current flows through the battery, affecting the terminal voltage.

What is the terminal voltage of a battery?

The terminal voltage is the actual voltage available to an external circuit when a battery is connected to a load. It is the net energy gained by a coulomb of charge as it moves through the battery, minus the energy lost due to the internal resistance.

How does the EMF of a battery differ from its terminal voltage?

The EMF is the total energy provided by the battery per coulomb of charge, while the terminal voltage is the actual voltage experienced by the external circuit, which is less than the EMF due to the energy lost as heat because of the internal resistance.

What happens to the terminal voltage when the current through a battery is zero?

When the current is zero, there is no heat loss due to internal resistance, so the terminal voltage equals the EMF of the battery, as all the energy provided by the battery is available to the external circuit.

Can you provide the mathematical equation that connects the EMF, internal resistance, current, and terminal voltage of a battery?

Yes, the equation is: VT = E - I * R, where VT is the terminal voltage, E is the EMF, I is the current, and R is the internal resistance of the battery.

Outlines

00:00

🔋 Understanding EMF, Terminal Voltage, and Internal Resistance

The first paragraph introduces the concepts of Electromotive Force (EMF), terminal voltage, and internal resistance of a cell. It sets up a scenario involving a battery and bulbs to illustrate how adding more bulbs in parallel leads to dimmer light, hinting at the relationship between current draw and voltage provided by the battery. The paragraph aims to clarify the confusion between EMF and terminal voltage and how they are connected through an expression involving internal resistance.

05:01

🚀 The Dynamics of EMF and Terminal Voltage

This paragraph delves into the specifics of EMF, explaining it as the energy transferred per coulomb by the battery, which is often marked on the battery itself. It then contrasts EMF with the actual energy a coulomb gains, taking into account the heat loss due to the internal resistance of the battery. The explanation uses an analogy of a parent pushing a child up a slide to convey the transfer of energy. The paragraph concludes by emphasizing that the terminal voltage is less than the EMF due to energy loss as heat and poses a question about the effect of moving the charge faster through the battery.

10:02

🔥 The Impact of Speed on Terminal Voltage

The final paragraph explores the effect of increasing the speed at which charge moves through the battery. It explains that as the charge moves faster, more heat is generated, leading to a greater energy loss and thus a lower terminal voltage. The paragraph reinforces the idea that the terminal voltage is the net energy gained by a coulomb after accounting for the heat loss due to internal resistance. It concludes with a formula that encapsulates the relationship between the internal resistance, current, EMF, and terminal voltage, emphasizing the importance of these factors in determining the energy dynamics within a battery.

Keywords

💡Electromotive Force (EMF)

Electromotive Force (EMF) is a term that refers to the electrical potential difference in a circuit, which is often indicated on a battery, such as 1.5V or 9V. It is a measure of the energy transferred by the battery per unit charge, expressed in joules per coulomb. In the context of the video, EMF represents the amount of energy the battery can provide to move a charge from one point to another within the circuit, which is crucial for understanding how a battery powers devices like bulbs.

💡Terminal Voltage

Terminal voltage is the actual voltage that appears across the terminals of a battery when it is connected in a circuit. It is the net energy gained by a unit charge as it moves through the circuit. The video explains that terminal voltage is typically less than the EMF due to energy losses, such as heat dissipation caused by the internal resistance of the battery. An example from the script is when a battery with an EMF of 9 volts has a terminal voltage of 7 volts due to 2 volts of energy being lost as heat.

💡Internal Resistance

Internal resistance is the resistance within the battery that opposes the flow of electric current. It is caused by the battery's chemical composition and physical structure. As explained in the video, when current flows through the battery, it encounters this internal resistance, leading to energy loss in the form of heat. This resistance affects the terminal voltage and is a key factor in the difference between EMF and terminal voltage.

💡Energy Transfer

Energy transfer in the context of the video refers to the process by which a battery imparts energy to an electric charge as it moves through the battery. This is analogous to a parent pushing a child up a slide, where the parent's push transfers energy to the child. In the case of a battery, the EMF represents the amount of energy transferred per unit charge, which is 9 joules per coulomb in the example provided.

💡Heat Loss

Heat loss is the energy dissipated as heat due to the internal resistance of the battery. As the current flows through the battery, it encounters resistance, which converts some of the electrical energy into thermal energy, thus reducing the energy available to do work externally. In the video, it is illustrated that out of the 9 joules of energy transferred by the battery, 2 joules are lost as heat, resulting in a terminal voltage of 7 volts.

💡Current

Current in the video refers to the flow of electric charge in a circuit, which is influenced by the EMF and the resistance in the circuit. The more current that flows, the more energy is drawn from the battery, and consequently, the more heat is generated due to the internal resistance. This increased heat generation leads to a drop in terminal voltage, as seen when additional bulbs are connected in parallel in the video's example.

💡Ohm's Law

Ohm's Law is a fundamental principle in electrical engineering that states the relationship between the voltage across a resistor (or any other electrical component), the current through it, and its resistance. In the video, Ohm's Law is used to explain the voltage drop across the internal resistance of the battery, which is given by the product of the current (I) and the resistance (R), represented as V = I * R.

💡Resistor

A resistor is a component in an electrical circuit that resists the flow of current. In the context of the video, the internal resistance of the battery is likened to a tiny resistor inside the battery. This resistor is not physically present but is a conceptual model used to represent the opposition to the flow of current within the battery, which results in heat loss and a reduction of the terminal voltage.

💡Energy Dissipation

Energy dissipation refers to the process by which energy is lost, typically in the form of heat, due to resistance in a circuit. In the video, energy dissipation is a key concept in understanding why the terminal voltage of a battery is less than its EMF. As current increases, more energy is lost as heat, leading to a lower terminal voltage.

💡Voltage Drop

Voltage drop is the decrease in voltage that occurs as current flows through a resistance, such as the internal resistance of a battery. The video explains that this voltage drop is equivalent to the heat loss per coulomb and is calculated using Ohm's Law (I * R). The voltage drop is a critical factor in the difference between the EMF and the terminal voltage of a battery.

💡Coulomb

A coulomb is the unit of electric charge in the International System of Units (SI). In the video, the energy transferred by the battery and the energy lost as heat are both discussed per coulomb. This unit is essential for quantifying the EMF and the terminal voltage, as it provides a measure of the energy per unit charge.

Highlights

EMF, or Electromotive force, is the energy transferred by a battery per coulomb and is typically indicated on the battery.

An increase in the number of bulbs connected in parallel to a battery results in a decrease in brightness due to higher current draw.

As more current is drawn from a battery, its terminal voltage decreases due to internal resistance and energy loss as heat.

The internal resistance of a battery causes energy loss as heat when current flows through it.

The terminal voltage of a battery is the actual energy gained by a coulomb of charge after accounting for energy lost as heat.

If the current through a battery is zero, there is no heat loss, and the terminal voltage equals the EMF.

The terminal voltage drops as the charge moves faster through the battery due to increased heat loss.

An equation relating the terminal voltage (VT), EMF (E), internal resistance (R), and current (I) is VT = E - I * R.

The concept of EMF is a misnomer as it measures energy, not force.

The battery pushes positive charges against electric repulsion, transferring energy into them.

The voltage provided by a battery starts reducing as more bulbs are connected in parallel, due to increased current draw.

The energy transferred by the battery is independent of the speed at which the charge moves through the battery.

When a battery is connected to a bulb, the bulb glows due to the flow of current.

The brightness of bulbs connected to an inverter decreases as more bulbs are turned on, illustrating the effect of current draw on voltage.

The voltage across the battery (terminal voltage) is the net energy gained by a charge after subtracting the energy lost due to internal resistance.

The heat generated inside a battery is a result of the resistance offered by the chemicals as the charge moves through them.

The terminal voltage of a battery can be almost equal to its EMF if the current is incredibly low, minimizing heat loss.

Transcripts

Let's explore the meaning of EMF, terminal voltage,

and internal resistance of a cell.

And see the difference between these two, which is always confusing for me.

And finally, we'll be able to write an expression connecting all of them.

So, let's begin.

Let's start by looking at a situation.

Imagine you have a battery connected to a bulb.

What happens?

It glows, no surprise.

But what will happen if I were to connect another identical bulb,

in parallel to this circuit.

What will happen?

Well, if you do that, you'll find that the bulbs will become dimmer.

If you attach one more bulb in parallel, it will become even dimmer.

This is something you may have experienced if you have inverters at home.

When the power goes off and your house is running on inverter,

you may have seen that as you switch on more and more tube lights,

the brightness decreases.

But why is this happening?

Or what does it mean?

Well, let's think about this.

As I start attaching more bulbs, I hope you agree that

more current starts getting drawn from the battery.

Does that make sense?

Because every bulb will start drawing current.

So, the thing that is happening as I attach more bulbs in parallel,

is that more current... Let me write that down over here.

More current

gets drawn from the battery.

Another way to see as to why more current gets drawn from the battery is...

Think about this.

When you attach more bulbs in, more resistors in parallel,

that effectual resistance decreases

Right?

And so, as the effectual resistance decreases, more current gets drawn.

And as you see, more circuits, more current gets drawn from the battery.

Alright, what happens because of that?

It turns out, because of that, the voltage provided by the battery starts reducing.

Again, let me clarify what I mean.

When I attach one bulb, I am drawing little current - high voltage.

As I attach another bulb, more current starts drawing from the battery -

the voltage reduces.

Put another bulb, even more current - voltage reduces even further.

So what's happening over here, for some mysterious reason,

which we have to figure out now is,

as you draw more current, the voltage across the battery drops.

And this is really confusing.

Why does that happen?

To answer this question we need to understand exactly

what EMF, terminal voltage, and internal resistance are.

So let's look at just one battery and a bulb.

Let me get rid of this.

And let's bring in just one battery and a bulb.

And start with a question of...

Let me just get rid of the bulb for now.

Let's start with the question of what is the meaning of EMF.

EMF is a number that is written on the battery, like 1.5V or 9V.

Let me just write that down.

So that is the EMF.

For example this could be a 9 volt battery.

So that 9 volt is the EMF.

And what does it mean?

EMF stands for Electromotive force.

And you can immediately see there is a problem with the wordings over here.

It's a force, it's named as a force, but it's not really a measure of force.

It's a measure of energy.

The name is stuck, it's a misnomer, but it's okay.

So let's think about what does this 9 volt mean?

What exactly is this?

For that we need to know what a battery does.

What does the battery do?

If I bring back that bulb... What the battery really does

is that it pushes charges.

Let me get an example of what I mean.

You might know that there are electrons all around.

But electrons are negative. I don't like negative.

So let me imagine there are positive charges.

Let's pick one positive charge.

With that positive charge over here, it gets repelled by this positive

or attracted by this negative, and as a result it falls like this.

Now, once inside the battery, notice the charge will not automatically go

from here to here.

No, no, there is a repulsion.

Now, what the battery does is the battery pushes this charge

against this electric repulsion.

And it pushes it, pushes it, pushes it and brings it over here.

Again, the whole thing falls.

Again, the battery pushes it, pushes it, and so on, and so forth.

In doing so... Why are the batteries pushing this charge?

I hope you agree, it's transferring energy into that charge.

This is very, very similar to how

when parents are pushing the child up onto a slide,

it transfers energy into that child

and then the child comes all the way down.

And again, the parental push...

The parent is like the battery

Pushing the child up transfers energy into that child.

Similarly over here, the battery transfers energy into this child.

Not child, charge.

And the EMF is a measure of that.

So what does it mean to say that the EMF is 9 volt?

It just means that the battery transfers

9 joules of energy

per coulomb.

So what that means is: if this was a one coulomb charge,

when it goes from here to here

the battery transfers 9 joules of energy to it.

So, are we clear with the word EMF?

Alright.

Now, let me ask you this question.

If this was one coulomb,

then when it goes from here to here

how much energy do you think the coulomb has gained?

It might be reasonable to think

that because the battery is transferring 9 joules of energy

the charge must have gained 9 joules of energy.

Just like over here.

When the parent does work, whatever energy it transfers,

gets transferred to the child as potential energy.

Maybe same thing is happening. Right?

This is where things get interesting.

Although... and this is where we need to be very careful.

Although the battery is transferring 9 joules of energy into the charge,

one thing to remember is that inside the battery,

there is a lot of chemical, a lot of material.

There is a lot of medium that can be wet, it can be dry,

but there is a lot of chemicals.

And as a result, as the charge moves through that chemicals,

the chemicals offer some resistance to it.

Just like when you move your hand through water,

it causes resistance.

Just like when you move through air, there is some resistance.

Similarly the chemicals inside the battery themselves resist the flow of charges.

And by the way, this resistance is called internal resistance

because it's a resistance inside the battery.

Internal to the battery.

Anyways, coming back to our story,

as the charge moves through this

there is heat generated.

Think about it. Whenever you move through any medium

because of the resistance there will be heat generated.

And as a result, some of the energy,

some energy is dissipated as heat.

The battery becomes hot.

For the sake of example, in this case let's say

out of that 9 joules transferred to the charge,

2 joules per coulomb, goes out as heat.

My question is: by the time the charge comes over here

how much energy does it have?

Well, it got 9 from the battery, but 2 got wasted as heat.

So what's remaining now is only 7 joules.

Only 7 joules per coulomb gets transferred eventually.

Therefore, every coulomb, when it comes from here to here,

only gains 7 joules.

And therefore, we now say that the voltage across the battery is 7 volt.

And this is what we call the terminal voltage.

This is the terminal voltage.

It's how much energy the coulomb finally gains.

You know? When it goes from here to here.

And hopefully now you see why the terminal voltage need not be equal to EMF,

or won't be equal to EMF -

because of the internal resistance there will be some heat loss.

Long story short, think of terminal voltage,

or the voltage of the battery,

as the energy gained by 1 coulomb as it goes from here to here,

that will be equal to the EMF, that is the energy transferred

by the battery per coulomb, minus the energy that is lost

due to heat due to the internal resistance.

If you understood this, I have a question for you.

My question now is: what if we had the same battery, with the same EMF,

with the same chemistry inside, meaning the same internal resistance,

but this time, what if we made the charge go faster through the battery.

What will then be the terminal voltage?

Would it be the same, 7 volt?

Would it be more than 7 or less than 7?

Can you pause the video and think about it?

Remember, same EMF, same internal resistance, same chemistry,

the charge is moving faster.

What happens with terminal voltage?

Pause and think about this.

Alright, if you've tried - because the EMF is the same,

the energy transferred when the coulomb goes from here to here is the same.

It doesn't matter whether you move it slowly or you move it fast.

The energy transferred by the battery is the EMF.

That remains the same.

That's 9 joules per coulomb.

Alright.

The internal resistance is the same

but the charge is moving faster through the medium.

Because of that, what happens to the heat energy formed?

When you move faster through any medium,

I hope you agree that the heat generated now is more.

And to give you an example, think about space shuttles

that are entering into our atmosphere.

You may have seen, maybe in movies,

that when they're going in an incredibly high speed,

they start heating up and burning.

Because of the high speed,

the heat generated is so high, they almost start burning.

But that doesn't happen for an airplane.

Why? Because they are going very slowly.

So when you go faster through any medium, and the medium is the same air,

but when you go faster through it, the heat generated is more.

So the same idea is applicable here as well.

As the charge moves faster through this battery,

more heat gets generated.

Maybe this time not 2, maybe, I don't know,

5 joules per coulomb is dissipated as heat.

More heat.

So now, what would be the new terminal voltage?

Out of 9, 5 got lost

so the new terminal voltage would only be 4.

So let me just write that over here.

4.

There are a lot of numbers but I hope you see what is going on over here.

What did we see?

As the charge goes faster, the terminal voltage drops.

Now can you answer our original question?

When you are drawing more current from the battery,

you're forcing the charges to go faster.

The energy supplied to the charge stays the same,

but as you go faster, the heat loss is more,

and therefore the terminal voltage drops.

Does that make sense now?

This is the reason why, as you attach more and more bulbs in parallel,

you are drawing more current, more heat loss,

and as a result, the voltage across the battery was dropping,

and therefore the bulb was going dimmer.

Similarly, if the charges move slower and slower,

then, I hope you agree, less heat will be lost

and more of that EMF will be over there, but as terminal voltage.

So the terminal voltage will increase.

What if the charges go very, very slow, incredibly slow.

At a snail's pace.

Almost not moving at all.

Then, almost no heat energy would be lost.

Then the terminal voltage would be almost equal to EMF.

Ah! So, do you now agree, do you now see why

if the current is zero, there will be no heat loss at all,

then all of the EMF would be available as terminal voltage.

So with current at zero, terminal voltage equals the EMF.

Does that make sense now?

Hopefully, we now have a clearer understanding of the difference

between the EMF and the terminal voltage, and why they differ,

and how internal resistance comes into the picture.

The last thing that I want to do is write this entire story into an equation. Okay?

For that, let's assume that the battery contains a tiny resistor inside of it

which represents its internal resistance.

There isn't any resistor, that's a model we like to work with.

So let's assume that there is a tiny resistor which represents the resistance,

our internal resistance of the battery.

The question now is:

if the current through this battery...

Let's give it some name.

If the current is I

what is the equation that connects all these variables?

The internal resistance, the current, the EMF, and the terminal voltage.

Use the same logic that we have used so far.

Alright, let me write it over here.

We don't need this anymore.

The way I think about this is: I know that the terminal voltage

is basically EMF minus the heat loss.

Let me write that over here.

The terminal voltage equals

the EMF

minus the heat loss.

And when I am saying heat loss, I am talking about heat lost per coulomb.

Right? Heat lost per coulomb.

So what I need to figure out is how do I calculate this heat loss per coulomb.

If you think carefully, this heat loss per coulomb is

the voltage across the resistor.

Think about it.

Whenever a current flows through the resistor, we say there is a voltage drop.

That voltage drop represents the energy dropped per coulomb.

And that energy dropped per coulomb is the heat energy per coulomb.

So this is basically the voltage across this resistor.

And from Ohm's law we know voltage across any resistor

would be just I times R.

And so we can now write our equation as

VT, the terminal voltage, equals

E, the EMF,

minus I times R.

And hopefully, this equation now makes a lot of sense to you.

This is the energy transferred by the battery per coulomb,

this is the heat energy lost per coulomb,

and the terminal voltage is the net energy gained per coulomb

as it goes from here to here.