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When learning about current sources and voltage sources, the concept of internal resistance often causes confusion. The key is to remember: when a voltage source is connected to an external load, its internal resistance is considered to be in **series** with the load. On the other hand, when a current source is connected to a load, its internal resistance is in **parallel** with the load. For a voltage source, the smaller the internal resistance, the better — because it allows for more efficient power delivery. For a current source, the larger the internal resistance, the better — as it helps maintain a more constant current. But why does this happen? What role does internal resistance play in a power supply? And why does maximum power transfer occur when the internal resistance matches the load?
Let’s start with some basic concepts:
1. A circuit consists of a power supply and a load.
2. A circuit can be divided into two parts: the internal circuit (inside the power supply) and the external circuit (the rest of the system).
3. Inside the power supply, there is a resistor that resists the flow of current. This is called the **internal resistance**.
4. Current passing through the internal resistance causes energy loss in the form of heat.
5. Internal resistance isn't just a waste of energy — it also causes the power supply to heat up, and in extreme cases, can lead to damage or failure.
6. The internal resistance of a power supply is essentially the resistance of the conductive materials inside it.
Now, let's explore why matching the internal resistance with the load leads to maximum power transfer.
A power supply has two main roles: it acts as an **energy source** for the load (like a battery), or as a **signal source** (like an audio amplifier). As an energy source, we want the internal resistance to be as small as possible so that more power is delivered to the load, improving efficiency. For example, generators, transformers, and power supplies are designed with low internal resistance.
As a signal source, however, we want the output power to be as high as possible. For instance, in an audio system, we want the speaker to produce the loudest sound. So, how do we achieve maximum power transfer from the signal source to the load?
- When the load resistance is much larger than the internal resistance, the power delivered to the load decreases, even though less energy is lost in the internal resistance.
- When the load resistance is much smaller than the internal resistance, more total power is generated, but most of it is lost in the internal resistance, leaving little for the load.
- Only when the load resistance is equal to the internal resistance does the power delivered to the load reach its **maximum**, which is 50% of the total power generated.
This is known as the **maximum power transfer theorem**.
Now, let’s look at voltage sources and current sources:
- A **voltage source** is designed to maintain a constant voltage across its terminals. To do this effectively, its internal resistance must be as small as possible. If the internal resistance is too large, the terminal voltage drops significantly under load.
- A **current source**, on the other hand, is designed to maintain a constant current regardless of the load. For this, the internal resistance should be as large as possible. This way, even if the load changes, the current remains relatively stable.
In practical terms, when analyzing complex circuits, real power supplies are often modeled as either:
- A **voltage source in series with an internal resistance**, or
- A **current source in parallel with an internal resistance**.
These models help simplify the analysis of real-world circuits.
To summarize:
- A **voltage source** works best when its internal resistance is small, allowing it to act like an ideal constant voltage source.
- A **current source** works best when its internal resistance is large, allowing it to act like an ideal constant current source.
- Matching the internal resistance with the load ensures maximum power transfer, but it’s not always the goal — depending on the application, you may prefer a low or high internal resistance.