Electrical Engineering

DC Circuit Analyzer

Analyze series and parallel resistive DC networks in real time: currents, voltages, power dissipation, and the maximum power transfer point.

DC circuits Thevenin Norton Max power transfer
Results Real-time
Load Power
—
W
Total Current
—
A
R-Thevenin
—
Ω
Efficiency η
—
%
Stable

Circuit physics active.

Circuit Diagram
RL Power Curve

Power delivered to RL vs. load resistance

Technical Results
ElementV (V)I (A)P (W)
Mathematical Analysis — Parallel Circuit Analysis
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About This Simulator

The DC Circuit Analyzer models a simple resistive network driven by an ideal DC voltage source V1, with a fixed resistor R1, a second resistor R2, and a variable load RL. Two topologies are supported: a series network, where R1, R2, and RL share a single current path, and a parallel network, where R1 acts as the source's series resistance and R2/RL share a common node.

Beyond basic current/voltage/power results, the simulator highlights the maximum power transfer theorem: for any fixed source and internal resistance, the power delivered to a variable load RL is maximized when RL equals the Thevenin resistance Rth seen from the load terminals. The RL Power Curve chart marks this optimal point directly on the graph.

How to Use

  1. Step 1. Choose the network topology — series or parallel.
  2. Step 2. Set the source voltage V1 and the values of R1 and R2.
  3. Step 3. Drag the RL slider and watch the KPIs and the RL Power Curve update in real time. The status banner tells you whether RL is above, below, or matched to the optimal load.
  4. Step 4. Open Guided Analysis to pick a resolution method (node voltages, mesh currents, Thevenin, Norton, or Delta–Wye) and see the equivalent diagram redrawn accordingly, alongside the full numeric derivation below.

Understanding the Results

Load Power (PRL)

The power dissipated by the variable load RL, in watts. This is the quantity maximized by the max power transfer theorem.

Total Current (Itotal)

The current delivered by the source V1, in amperes.

R-Thevenin

The equivalent resistance of the source network as seen from the RL terminals, with the source shorted and the load removed. RL = Rth is the load value that maximizes power transfer.

Efficiency η

The fraction of total source power that reaches the load (η = PRL / Psource). Efficiency and maximum power transfer are not the same goal: efficiency keeps improving as RL grows, while power transfer peaks at RL = Rth and then decreases.

Frequently Asked Questions

What does RL = Rth actually mean?
It means the load resistance matches the Thevenin resistance of the source network seen from the load terminals. At that point, the power delivered to the load is at its maximum possible value for the given source and internal resistances — though efficiency at that point is always exactly 50%.
Why does higher RL give better efficiency but less power?
As RL increases beyond Rth, more of the source voltage appears across the load and less is lost internally, so efficiency rises toward 100%. But the total current drops, and since power depends on both current and voltage, the actual watts delivered to the load decrease past the optimal point.
What's the difference between the series and parallel topology here?
In the series topology, R1, R2, and RL all carry the same current. In the parallel topology, R1 sits between the source and a node where R2 and RL are connected in parallel, so R2 and RL share the same node voltage but carry different currents.
What are the limitations of this simulator?
The source is modeled as an ideal DC voltage source (zero internal resistance of its own — R1 represents any source/line resistance explicitly). All components are assumed linear and time-invariant; transients, reactive elements, and non-ideal sources are outside the scope of this model.