what is ideal Voltage and Current Sources?: Formula, Symbol

ideal Voltage and Current Sources

Electricity is a part of our daily life. We use it to light our homes, run our fans, charge our phones, and power our TVs. But have you ever thought — where does this electricity come from? That’s where voltage sources and current sources come in. Let’s understand them in the most simple and natural way.

🌟 What is a Voltage Source?

A voltage source is something that gives us a push to move electric charges in a wire. This push is called voltage.

You can think of it like this:
Imagine water flowing through a pipe. To make the water move, you need pressure. In the same way, to move electric charges (we call this flow “current”), we need voltage.

Some everyday voltage sources include:

• Batteries (like AA or mobile batteries)
• Generators
• Alternators in vehicles

These are called active elements because they supply energy to the circuit.

💡 So, a voltage source is simply something that creates a difference in electrical pressure across its ends, which allows electricity to flow.

⚡ What is a Current Source?

Now let’s talk about a current source.

A current source is a device that provides a constant flow of electric current, no matter what. Even if the load changes (like a fan running faster or slower), a current source tries to keep the same amount of current flowing.

These are not as easy to imagine as voltage sources, but they are used in many electronic circuits — for example, in the collector part of a transistor.

Just like voltage sources, current sources also give energy, so they are also called active elements.

🔄Different ideal Voltage and Current Sources

Fun Fact: A current source can always be converted into a voltage source, and vice versa. This helps engineers solve circuit problems easily!

Ideal Voltage Source (Constant-Voltage Source) –

An ideal voltage source is a very special type of power source. It always gives the same voltage, no matter how much current you take from it. That’s why it is also called a constant-voltage source.

Imagine you have a battery that always shows 12 volts on its terminals. If you connect a big resistor or a small one, or even a motor — the voltage stays fixed at 12V. It never drops or changes. That’s what we call an ideal voltage source.

✅ Main Feature of an Ideal Voltage Source:

• It has zero internal resistance.
• So, no voltage is lost inside the source.
• You get full voltage directly at the output — all the time.

🧠 Let’s Understand with an Example:

Suppose we have an ideal voltage source of 12 volts.

See? No matter how small or large the load is, the voltage stays at 12 volts.

❗But Wait! Is it Real?

No. In real life, perfect voltage sources don’t exist.
Every battery or power supply has a small internal resistance. This tiny resistance causes a small voltage drop when current flows. So, the terminal voltage goes down a little.

⚡ Practical Example of a Constant Voltage Source

Let’s take a 6V battery with internal resistance of just 0.005 ohms. Even if the current changes from 1A to 10A, the voltage drop is very small:

Voltage drop = Current × Internal resistance
At 10A: 10 × 0.005 = 0.05V
So, output voltage = 6V – 0.05V = 5.95V

That’s still very close to 6 volts. So, we can treat it like a constant-voltage source.

🔋 Real-Life Example: Lead-Acid Battery

A lead-acid cell is a great example of a practical constant-voltage source.
Its internal resistance is very low (about 0.01 ohms), so it gives almost the same voltage even if the load changes.

🔷 Symbol of Constant Voltage Source

A constant voltage source is shown like this:

   + ──────( ⊕ )────── -

This shows that the voltage remains fixed and steady across the terminals.

📌 Key Points to Remember

• An ideal voltage source always gives constant terminal voltage.
• It has zero internal resistance.
• In real life, every source has some resistance.
• If the resistance is very small, it acts like a constant-voltage source.
• Lead-acid cells are a real-world example of this.
  
  

Real Voltage Source

A real voltage source is something we use in electrical circuits every day. But unlike an ideal voltage source (which is perfect), a real one is not perfect. It has a small resistance inside it, called internal resistance (we write it as Rint).

Because of this resistance:

• When we connect a load and draw more current, the output voltage drops.
• If we reduce the current, the output voltage increases again.

So, the voltage we get depends on how much current we are taking from the source.

Let’s understand this in a very easy way:

🌟 What is a Real Voltage Source?

A real voltage source is a power supply that gives out electricity (voltage), just like a battery. But it has a small internal resistance inside. Because of this resistance, the voltage at its terminals drops a little when we connect something to it.

🧠 How Does It Work?

When you connect a load (something like a bulb or motor), current starts flowing. But the internal resistance (Rint) of the source resists this current a little. So, the voltage you get at the end is less than what it was without the load.

Formula real voltage source

When a load (RL) is connected, the current IL flows in the circuit.
The output voltage (Vo) is given by this simple formula:

Vo = E – IL × Rint

Where:

• E = voltage of ideal source (when no current flows)
• IL = current flowing in the circuit
• Rint = internal resistance
• Vo = output voltage we actually get

Important to Know

• The smaller the internal resistance, the better the voltage source.
• If Rint is almost zero, then the real voltage source acts like an ideal one.
• In most basic circuit calculations, we assume the voltage source is ideal because it makes the math easier. And for small changes in current, this assumption works fine.

🧠 Summary

• A real voltage source gives power, but it has a small internal resistance.
• Because of this, the voltage output changes with the load current.
• It can be shown as an ideal source + a small resistor in series.
• The smaller the internal resistance, the closer it behaves to an ideal source.

Ideal Current Source

An ideal current source is a very special type of power source. It always gives the same amount of current no matter what is connected to it.

Imagine this:
You have a tap that always gives exactly 2 liters of water every second, no matter if the pipe is thin or wide. In the same way, an ideal current source always sends the same current, whether the wire connected to it is thick or thin.

What Makes It Special?

• An ideal current source never changes the current.
• Even if you connect a small bulb or a big machine, the current stays the same.
• It doesn’t matter how big or small the resistance is — the current never changes.

Internal Resistance is Infinite

This means inside the source, it behaves like there is an infinite wall stopping any change in current.
Because of this, it always controls the current perfectly.

How Does Voltage Change?

The current stays the same, but the voltage can change depending on the resistance.

Let’s understand with an example:

• If the current source gives 2 Amperes and the resistance is 10 ohms,
  Voltage = 2 × 10 = 20 volts
• If the resistance becomes 100 ohms,
  Voltage = 2 × 100 = 200 volts

So, the voltage changes, but the current remains fixed.

Symbol of Ideal Current Source

The symbol looks like a circle with an arrow.
The arrow shows the direction of current.

Why is it Called “Ideal”?

Because in real life, no current source is perfect.
But an ideal current source is just a perfect model.
It helps us understand circuits in a simple way during study or design.

Quick Summary

✅ Always gives the same current
✅ Doesn’t care what load is connected
✅ Has infinite internal resistance
✅ Voltage changes based on resistance
✅ Symbol: Circle with arrow
✅ Used in theory and learning for easy understanding

Real Current Source

A real current source is a device that gives current to a circuit. But unlike a perfect (ideal) current source, a real one is not 100% perfect — and that’s okay! Let’s understand why.

✅ What Is a Real Current Source?

A real current source gives a current that almost stays constant, but slightly changes when the load changes. This happens because it has a small internal resistance inside it. Think of it like this:

• An ideal current source always gives the same current — no matter what.
• A real current source tries to do the same, but due to its internal resistance (Rint), the current going to the load can change.

🔧 How Does It Work?

You can imagine a real current source as:

👉 An ideal current source in parallel with a resistor (called internal resistance Rint).

When you connect a load resistor (RL) to it, the total current splits:

• Some goes through the load.
• Some goes through the internal resistor.

That’s why the load current (IL) becomes less than the total current (I).

We can find the load current using this formula:

IL=I−V/Rint

Where:

• IL is the load current,
• I is the current from the ideal source,
• V is the voltage across the load,
• Rint is the internal resistance.

📈 Real Current Source Graph

If we draw a graph of load current (IL) vs output voltage (V):

• The graph slopes downward.
• This shows that when voltage increases, the load current slightly drops.
• A real source gives less current than an ideal one.

✅ Good to Know:

• Higher internal resistance = Closer to ideal current source.
• Real sources can be combined:
  • If two real current sources are giving current in same direction, total current = sum.
  • If they’re in opposite directions, total current = difference.
    

Source Conversion – Voltage Source to Current Source

In electricity, there are two types of sources: voltage source and current source. But did you know that we can convert one into the other without changing anything for the connected circuit? Yes! This is called source conversion or source transformation.

Let’s understand it in a super simple way.

⚡ What is a Voltage Source?

A voltage source gives a fixed voltage. But in real life, it also has an internal resistance inside it. So, we draw it like this:

👉 Voltage Source (E) in series with internal resistance (Rint).

When we connect a load (something that uses electricity, like a bulb or fan), some current flows through the circuit. That current is called the load current (IL).

🔄 How to Convert a Voltage Source into a Current Source?

We can convert the above voltage source into an equivalent current source. That means both circuits will give the same results, even though they look different.

Here’s how we do it:

1. First, we find the short-circuit current (IS). This is the current that flows if the voltage source is shorted (like connecting the two ends directly).
2. ✏️ Formula: IS=ERint
3. Now, we draw a current source (IS) in parallel with the same internal resistance (Rint).

That’s it! This is the equivalent current source of the real voltage source.

🔁 Are They Really the Same?

Yes! Both circuits are exactly the same in how they behave. You can connect any device to either one, and you’ll get the same current, same voltage, and same results.

You cannot tell whether it’s a voltage source or current source just by looking from outside or measuring anything — they are completely equivalent.

✅ Summary: Voltage to Current Source Conversion

📘 Why is Source Conversion Useful?

• It makes circuit analysis easier.
• Helps in Thevenin and Norton’s theorems.
• Useful in simplifying complex electrical networks.
  
  

Current to Voltage Source Conversion –

Sometimes in electric circuits, we need to change a current source into a voltage source to make things easier to understand or solve. This trick is called source conversion.

Let’s learn this step by step in a way even a small child can understand. 😊

🔌 What is a Current Source?

A current source is something that gives a constant current no matter what is connected to it. Imagine a tap that always gives the same flow of water – that’s like a current source.

But in real life, a current source is not perfect. It has a parallel resistance with it, called R_int (internal resistance).

⚡ What is a Voltage Source?

A voltage source gives a fixed voltage, just like a battery. But it also has a resistance inside it, in series with the voltage, which we also call R_int.

🔁 How to Convert Current Source to Voltage Source?

Now here’s the magic:

• Suppose we have a current source of I_S (ampere) with a parallel resistance R_int.
• We can convert this into a voltage source.

✅ The formula is:

E = I_S × R_int

Here,

• E is the voltage of the new voltage source,
• R_int is still the internal resistance,
• and it will now be in series with the voltage source.

So the voltage source will have:

• Voltage = E
• Series resistance = R_int

🎯 Why Do We Convert Sources?

Because sometimes a circuit becomes easier to understand or solve if we switch from one type of source to another.

• You can change a voltage source into a current source too.
• And any resistor connected with the source can be included in the conversion.

🧠 Final Tip to Remember

Both the original current source and the converted voltage source will behave exactly the same in a circuit. That’s why we say they are equivalent.

So next time you see a current source with a parallel resistor, just multiply the current and resistance, and you’ll get the voltage for the new voltage source!

✅ Summary (Easy to Remember):

Dependent Voltage and Current Sources

In electrical circuits, some sources don’t work on their own. They depend on something else—like another voltage or current—in the circuit. These are called dependent sources.

They are very important in designing amplifiers, transistors, and many automatic circuits.

💡 What is a Dependent Source?

A dependent source gives voltage or current at its output.
But it doesn’t work independently. It depends on another voltage or current somewhere else in the circuit.

Think of it like this:
If a machine gives output only when another machine is working, it is “dependent.”
Similarly, these sources work only when they get a signal (voltage or current) from another part of the circuit.

🔷 Symbol of Dependent Sources

All dependent sources are shown with a diamond-shaped symbol.
This helps you easily identify them in circuit diagrams.

✅ Types of Dependent Sources

There are 4 main types of dependent sources, based on what they depend on and what they give as output:

Voltage-dependent voltage source
Voltage-dependent current source

Current-dependent voltage source
Current-dependent current source

Voltage-Dependent Voltage Source (VDVS) –

A voltage-dependent voltage source is a special kind of source that gives voltage at its output, but it doesn’t decide on its own. It listens to another voltage at the input and works only according to that.

That’s why we call it “dependent.”
It depends on another voltage to work.

💡 What Does It Mean?

Think of a microphone and speaker:

• The microphone takes in your voice (input voltage)
• The speaker gives out a louder version (output voltage)

If you speak louder (more input voltage), the speaker becomes louder too (more output voltage).
That’s how a voltage-dependent voltage source works.

🔧 How It Works

There is a constant multiplier, let’s call it A (gain), which tells the source how much louder (or higher) the output voltage should be compared to the input.

📐 Formula:

v0=A×v1

Where:

• v₀ = Output voltage
• v₁ = Input voltage
• A = Constant multiplier (dimensionless)

✅ Easy Example

Let’s say:

• v₁ = 20 mV (millivolts)
• A = 60

Then: v0=60×20 mV=1.2 V

If v₁ changes to 30 mV, then: v0=60×30 mV=1.8 V

So, as the input voltage increases, the output voltage increases in the same ratio.

🔍 Where Is This Used?

• In amplifiers
• In audio systems
• In communication devices
• In automatic control circuits

This type of source is used when we need to amplify or change voltages without using external power.

📌 Key Points to Remember

Current-Dependent Voltage Source (CDVS) –

A current-dependent voltage source is a type of source that gives voltage at its output, but only when there’s a current at its input. That’s why it’s called dependent—it depends on another current in the circuit.

💡 What Does It Actually Do?

Imagine you’re pedaling a bicycle with a headlight. The faster you pedal (more current), the brighter the light (more voltage).
This is exactly what a current-dependent voltage source does:

It gives out voltage based on how much input current is flowing.

🔧 How It Works

We use a constant, usually called k or sometimes β, to calculate how much output voltage will be created.

📐 Formula:

v0=k×i

Where:

• v₀ = Output voltage
• i₁ = Input current
• k = Constant (with units of V/A, also known as ohms)

✅ Easy Example

Let’s say:

• Input current i₁ = 50 µA (microamperes)
• Constant k = 0.5 V/A

Then: v0=0.5×50 μA=0.5×50×10−6=25 μV

If i₁ becomes 20 µA, then: v0=0.5×20×10−6=10 μV

So, more current at the input gives more voltage at the output—and less current gives less voltage.

🔍 Where is It Used?

• In transistor circuits
• In sensor amplifiers
• In analog signal processing
• In feedback loops

This type of source is often used to convert current signals into voltage, which helps circuits work more accurately.

📌 Key Points to Remember

🧠 In Simple Words

A current-dependent voltage source is like a lamp that gets brighter when you pedal faster.
It turns current into voltage using a constant multiplier (k).

Voltage-Dependent Current Source (VDCS)

A voltage-dependent current source is a special type of source that gives current at its output, but only when it receives voltage at its input.

In other words, it doesn’t work on its own.
It depends on a voltage signal (v₁) to decide how much current (i) it should give out.

💡 What Does It Mean?

Imagine a water tap that gives water only when you turn the handle (which is like giving voltage). The more you turn, the more water flows. That’s exactly what this current source does—it gives more current when the input voltage increases.

🔧 How Does It Work?

We use a constant, often written as G, S, or in siemens (S), to calculate how much output current will be produced.

📐 Formula:

i=G×v1

Where:

• i = Output current
• v₁ = Input voltage
• G = Conductance (in siemens, which means A/V)

✅ Example Made Simple

Let’s say:

• Input voltage v₁ = 10 mV
• Constant G = 0.2 siemen (S)

Then: i=0.2 S×10 mV=0.2×0.01 V=2 mA

So, the output current is 2 milliamperes.

If the voltage increases, current increases too. If voltage drops, current drops.

🔍 Where is This Used?

• In operational amplifiers
• In field-effect transistors (FETs)
• In analog signal circuits
• In automatic gain controls

These sources help convert voltage signals into current, which is very useful in many devices.

📌 Key Points to Remember

🧠 In Simple Words

A voltage-dependent current source gives current as an output, but only when voltage tells it to.
More voltage = more current. Less voltage = less current.

Current-Dependent Current Source (CDCS) –

A current-dependent current source is a type of electrical source that gives current at its output, but only when another current tells it to. That’s why we call it dependent—because it depends on another current in the same circuit.

💡 What Does It Really Mean?

Imagine two water pipes connected together.

• If more water flows in the first pipe (input current),
• The second pipe (output current) also starts flowing more strongly.

That’s exactly what happens in a current-dependent current source.

🔧 How Does It Work?

Let’s say we have an input current, i₁.

The source uses a constant multiplier, called β (beta), to decide how much output current, i, it should give.

📐 Formula:

i=β×i1

β has no unit. It’s a simple number like 10, 50, or 100.

✅ Example Made Simple

Let’s say:

• Input current i₁ = 50 µA (microamperes)
• Constant β = 100

Then:

i=100×50 μA=5000 μA=5 mA

Now, if input current i₁ drops to 20 µA, then:

i=100×20 μA=2 mA

💡 As the input current changes, the output current changes in the same way.

🔍 Where is This Used?

• In transistors (like in amplifiers)
• In current mirrors in analog circuits
• In signal processing
• In feedback systems

It’s one of the building blocks of electronic devices.

📌 Key Points to Remember

🧠 In Simple Words

A current-dependent current source is like a shadow—it follows the input current. If input increases, output increases. If input goes down, output follows it.

Why Are Dependent Sources Important?

Dependent sources are used in:

• Amplifiers
• Transistors
• Op-amps
• Electronic circuits

Without dependent sources, we can’t control signals or build smart circuits.

They make sure our circuit responds and adjusts based on what’s happening inside it.

📌 In Simple Words:

Independent Voltage and Current Sources

📘 Basic Electrical Engineering – Explained Simply Like Never Before!

In every electrical circuit, we need a source that gives energy.
Some sources work on their own, without depending on any other part of the circuit.
These are called independent sources — and they are the most basic building blocks in electronics.

🔋 What is an Independent Source?

An independent source gives either:

• a voltage (electrical pressure), or
• a current (flow of electricity)

…without caring what else is happening in the circuit.
It works on its own, always giving the amount it’s supposed to give.

🔸 1. Independent Voltage Source

An independent voltage source gives a fixed voltage between its two terminals.

Example: A battery, a generator, or a power supply.

• It always keeps the same voltage no matter what load is connected.
• The voltage can be constant (DC like a 9V battery) or changing with time (AC like 230V household supply).

✅ Important Points:

• It has two terminals.
• The positive terminal is at a higher potential.
• If the voltage is positive (v > 0), current flows from the positive to the negative terminal.

📐 Symbol:

A circle with a plus (+) and minus (–) sign or labeled V for DC and v(t) for time-varying voltage.

🔸 2. Independent Current Source

An independent current source gives a constant current through the circuit.

Example: A constant current power supply used in LED lighting.

• It forces the current through the circuit even if the voltage across it changes.
• The current can also be steady (I) or time-varying (i(t)).

✅ Important Points:

• It has two terminals.
• The arrow shows the direction of current flow.
• The voltage across it adjusts automatically to maintain the given current.

📐 Symbol:

A circle with an arrow inside, labeled I or i(t) depending on whether it is constant or changing with time.

🧠 Easy Way to Remember

🧲 Where Are These Used?

• Batteries – Provide constant voltage (independent voltage source)
• Solar cells – Can act as voltage sources
• LED drivers – Often use constant current sources
• Power supplies – Have both voltage and current settings

🎯 Real-Life Analogy

• A voltage source is like a water pump that maintains constant pressure, no matter how much water you use.
• A current source is like a tap that always gives the same amount of water per second, even if the pipe size changes.
  
  

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