Power Supplies: EMF and Internal Resistance

A power supply is an element that delivers controlled electrical energy to a circuit.

So far we have discussed resistors, capacitors, and inductors: passive components that dissipate or store energy. Where does that energy come from?

We need an active element. We need a Power Supply.

You might think: “Luis, this is easy. A 9V battery gives 9V. Period.” Well, I’m sorry to tell you that you’ve been lied to. In the real world, no source is perfect, and its voltage depends on the load and its regulation.

EMF and Terminal Voltage

Suppose you have a car battery with a nominal voltage of 12 V. If you measure it in an open circuit and it’s charged, you can get around 12.6 V, depending on its condition and technology.

But, the moment you start the car (when the starter motor demands a lot of current), if you look at the multimeter, you will see that the voltage drops to 10V or 9V.

What happened? Did the battery suddenly drain? No. Reality simply kicked in.

The Electromotive Force ( or EMF)

This is the “ideal” voltage of the source. It is the maximum chemical or mechanical capacity the generator has to separate charges.

• It is the value we measure at no load (open circuit, I = 0).
• It’s what’s on the label: 12V.

The Terminal Voltage ()

This is the actual voltage available to your circuit when you are drawing current.

• It is what we measure with the load connected.

Why are they different? Because of the Internal Resistance.

The Internal Resistance ()

Inside the battery, there’s no ideal behavior. There are electrolytes, lead plates, metal connections… All of that has resistance.

As a first approximation, we model a battery using two elements:

1. A perfect Ideal Source (the EMF).
2. An internal resistance () in series.

This is a useful model, although the actual impedance also changes with temperature, state of charge, aging, and frequency.

When we draw current () from the battery, this current must necessarily pass through the internal resistance (). And, according to Ohm’s Law, an internal voltage drop occurs:

Therefore, the voltage that goes out to the external world is:

In other words, no real source is perfect. It always has a limit, and understanding this limit prevents many headaches when designing or diagnosing a circuit.

Voltage and Current Sources

In theoretical problems and simulators, you will see two distinct models. It is important not to confuse them.

Voltage Sources

These are the most common. Batteries, car batteries, home wall outlets.

• Goal: They try to maintain a Constant Voltage, regardless of what you connect.
• Ideal: Always gives X Volts, even if the current is infinite (physically impossible).
• Real: The voltage drops a bit when the load increases (due to the internal resistance we just saw).

Example: Your home’s electrical grid gives you 230V. If you turn on the washing machine (you draw current), the grid tries to keep giving you 230V.

Current Sources

These are the great unknowns for beginners, but they are fundamental in modern electronics (LED drivers, transistors).

• Goal: They try to maintain a Constant Current, varying the voltage as necessary.
• Behavior:
  • If you put a 10Ω resistor and the source is set to 1A, it will adjust its voltage to 10V.
  • If you change the resistor to 100Ω, the source will automatically raise its voltage to 100V to force 1A to keep flowing.

Comparative Summary