A source of electricity is an active circuit element that delivers energy to a network by converting non-electrical energy into electrical potential (voltage) or electron flow (current). When you define sources of electricity in circuit analysis, you are establishing the 'forcing function'—the baseline excitation that dictates every subsequent voltage drop, current branch, and power dissipation in the entire network. Beginners commonly confuse an ideal voltage source (a mathematical abstraction that supplies infinite current to maintain its voltage) with a real-world power supply (which has strict current limits, internal resistance, and foldback protection). Understanding this distinction is the difference between a simulation that works perfectly in LTspice and a physical prototype that melts your breadboard.
The Core Taxonomy: How We Define Sources of Electricity
In network theory, we categorize sources based on two axes: what they regulate (voltage or current) and what controls their output (independent or dependent). According to foundational circuit theory taught in programs like MIT's OpenCourseWare Circuits and Electronics, dependent sources are the mathematical building blocks we use to model active semiconductor devices like transistors and op-amps.
| Source Type | Symbol / Abbreviation | Output Rule | Real-World Equivalent |
|---|---|---|---|
| Independent Voltage | V (Circle) | Maintains fixed V regardless of I | Battery, Bench Supply (CV mode) |
| Independent Current | I (Circle) | Maintains fixed I regardless of V | LED Driver, Solar Panel (at Vmp) |
| Voltage-Controlled Voltage Source | VCVS (Diamond) | V_out = μ * V_control | Op-Amp (ideal model), Transformer |
| Current-Controlled Voltage Source | CCVS (Diamond) | V_out = r * I_control | Hall Effect Sensor, Transimpedance Amp |
| Voltage-Controlled Current Source | VCCS (Diamond) | I_out = g * V_control | MOSFET (saturation region model) |
| Current-Controlled Current Source | CCCS (Diamond) | I_out = β * I_control | BJT Transistor (small-signal model) |
Think of an independent current source like a metered ramp on a highway—it forces exactly 50 cars per minute onto the road, regardless of how fast they eventually travel or how much traffic backs up (voltage). It will push as hard as it needs to (raise its voltage) to maintain that exact flow rate.
Ideal vs. Practical: The Internal Resistance Reality Check
On paper, an ideal 12V voltage source outputs exactly 12.000V whether you draw 1mA or 10,000A. In reality, every physical source has internal resistance (often denoted as $R_i$ or $R_s$). As Georgia State University's HyperPhysics notes regarding electromotive force (EMF), the terminal voltage of a real source drops as current increases due to this internal resistance.
Worked Numeric Example:
Imagine a 12V lead-acid battery with an internal resistance of 0.2Ω. You connect it to a heavy load that measures 1.0Ω.
- Total Circuit Resistance: $R_{total} = 1.0Ω (load) + 0.2Ω (internal) = 1.2Ω$
- Circuit Current: $I = 12V / 1.2Ω = 10A$
- Voltage at the Load: $V_{load} = 10A * 1.0Ω = 10V$
- Internal Voltage Drop: $V_{internal} = 10A * 0.2Ω = 2V$
The load only sees 10V, not 12V. Furthermore, the battery is internally dissipating $P = I^2 * R = 100 * 0.2 = 20W$ as heat. If you ignored the internal resistance and assumed an ideal source, you would have calculated a load current of 12A and missed the 20W thermal loss entirely.
Where You Meet This in Practice
You don't just see these concepts in textbooks; you interact with them every time you power up a project on the workbench.
Voltage Sources (CV Mode)
Your bench power supply (like a Rigol DP832 or Korad KA3005P) in Constant Voltage mode acts as a practical voltage source. It tries to hold the voltage steady, but if your circuit pulls more current than the supply's limit (e.g., 5A), the supply's internal protection kicks in, dropping the voltage to fold back the current. Batteries, such as a 12V 100Ah LiFePO4 pack, are also voltage sources, though their open-circuit voltage sags based on their State of Charge (SoC) and internal cell impedance.
Current Sources (CC Mode)
Dedicated LED drivers (like the Mean Well HLG-120H-C1400) are engineered to be current sources. They will automatically adjust their output voltage anywhere between 50V and 100V to ensure exactly 1400mA flows through the LED string. Similarly, when you use an electronic load (like a Rigol DL3021) in Constant Current (CC) mode to test a battery, the electronic load acts as a programmable current sink (a negative current source).
Dependent Sources (Semiconductors)
You cannot buy a 'VCCS' module off the shelf. However, when you bias an N-channel MOSFET like the IRF540N into its saturation region, the drain current becomes a Voltage-Controlled Current Source, dictated by the gate-to-source voltage ($V_{gs}$) and the transistor's transconductance ($g_m$).
Real-World Scenario Walkthrough: The High-Power LED Burnout
Misunderstanding the difference between an ideal voltage source and a practical current source is a classic way to destroy expensive components. Here is a scenario from the bench.
1. The Setup: You want to test a bare 100W COB (Chip-on-Board) LED array. The datasheet states the nominal forward voltage is 30V at 3A. You wire it directly to a bench power supply capable of 60V at 5A.
2. The Numbers: You set the bench supply to Constant Voltage (CV) mode at 32V, assuming the 2V overhead will safely drive the LED to its 3A rated current.
3. The Outcome: You flip the output on. The LED flashes blindingly bright for about two seconds, then emits a sharp crack, goes dark, and the phosphor coating bubbles. The power supply trips its over-current protection at 5A.
4. What Went Wrong: You treated the bench supply as an ideal voltage source and the LED as a simple resistor. In reality, LEDs have a highly non-linear, exponential V-I curve and a negative temperature coefficient. As the LED heated up, its forward voltage dropped. Because the supply was forcing a fixed 32V (acting as a stiff voltage source), the current skyrocketed past 3A, causing thermal runaway. The supply didn't limit the current fast enough to save the die.
The Fix: Switch the bench supply to Constant Current (CC) mode and set the limit to 3.0A. The supply will now act as a current source, automatically dropping its voltage to whatever the LED requires (likely around 29.5V once warm) to maintain exactly 3A.
Frequently Asked Questions
Can a power supply be both a voltage and current source?
Yes, but not simultaneously in the way an ideal mathematical model suggests. Modern bench supplies operate in either CV (Constant Voltage) or CC (Constant Current) mode depending on the load. The supply continuously monitors the output and defaults to whichever mode limits the output to the user-defined thresholds. If your load draws less than the CC limit, the supply acts as a voltage source. If the load tries to draw more, the supply crosses over and acts as a current source.
Why do we use dependent sources if they don't exist as physical parts?
Dependent sources are mathematical abstractions used to model the internal behavior of active components. When you look at the 'hybrid-pi' small-signal model of a 2N3904 BJT transistor, the collector-emitter path is modeled as a CCCS (Current-Controlled Current Source). This allows engineers to use linear circuit analysis techniques (like Kirchhoff's laws and superposition) to calculate the gain and impedance of amplifier circuits without solving complex non-linear semiconductor physics equations.
What happens if you short-circuit an ideal current source?
In theory, an ideal current source short-circuited with a 0Ω wire will simply push its rated current through the short, developing 0V across its terminals. It operates perfectly fine. However, if you open-circuit an ideal current source, it will attempt to push its current through infinite resistance, theoretically generating infinite voltage. In the real world, a physical current source (like a solar panel or LED driver) will simply hit its maximum voltage compliance limit and clamp there, often triggering an over-voltage protection fault.
