Voltage Sources and Current Sources (DC)

In an electrical circuit, a source is required to generate voltage and current. In direct current (DC), there are two widely used idealized models:

• the voltage source,
• the current source.

These models simplify circuit analysis and help us understand the actual behavior of power sources (batteries, power supplies, photovoltaic modules, etc.).

1. Ideal voltage source

An ideal voltage source maintains a constant voltage across its two terminals, regardless of the current flowing through it (within certain limits).

• Examples:
  • \(12\ \mathrm{V}\) battery (simplified model)
  • laboratory power supply set to \(5\ \mathrm{V}\)

• The symbol is often a generator with the voltage noted next to it (e.g., \(12\ \mathrm{V}\)).

In this model:

• the voltage \(U\) is fixed (for example, \(12\ \mathrm{V}\)),
• the current \(I\) adjusts depending on the circuit’s resistance.

Example:

• \(U = 12\ \mathrm{V}\)
• If we connect \(R = 6\ \mathrm{\Omega}\) → \(I = 12 / 6 = 2\ \mathrm{A}\)
• If we connect \(R = 3\ \mathrm{\Omega}\) → \(I = 12 / 3 = 4\ \mathrm{A}\)

The source "provides what is needed" in terms of current to maintain \(12\ \mathrm{V}\) (as long as it can).

2. Ideal Current Source

An ideal current source imposes a constant current in the circuit, regardless of the voltage across its terminals (within certain limits).

• It is modeled as a fixed current symbol \(I\) (for example, \(2\ \mathrm{A}\)).

In this model:

• the current \(I\) is fixed (for example, \(2\ \mathrm{A}\)),
• the voltage \(U\) adjusts according to the resistance of the circuit.

Example:

• \(I = 2\ \mathrm{A}\)
• If we connect \(R = 4\ \mathrm{\Omega}\) → \(U = R \times I = 4 \times 2 = 8\ \mathrm{V}\)
• If we connect \(R = 10\ \mathrm{\Omega}\) → \(U = 10 \times 2 = 20\ \mathrm{V}\)

The source "adjusts" the voltage to keep the current constant (as long as it is capable of doing so).

3. Real-world generators

In reality, no source is perfectly ideal:

• a battery cannot supply infinite current, nor maintain exactly \(12\ \mathrm{V}\) under any load;
• a current generator has a maximum voltage beyond which it breaks down.

Real sources are often modeled with:

• an ideal voltage source + a small internal resistance in series, or an ideal current source + an internal resistance in parallel.

4. Connection to photovoltaics (overview)

The photovoltaic module behaves:

• more like a current source in part of its \(I\)–\(V\) curve (nearly constant current over a wide voltage range),
• then more like a voltage source around the open-circuit voltage.

In this chapter on general electricity, the key takeaway is:

Some generators behave more like a voltage source (battery, power supply).

Others sometimes behave like a current source (PV modules under certain conditions, current generators).

The chapters on photovoltaics will detail this \(I\)–\(V\) curve and the maximum power point (MPP).