Thévenin Equivalent Circuit Builder

Circuit Parameters

Source voltage V_s 12.0 V

Series resistance R1 50 Ω

Parallel resistance R2 100 Ω

Load resistance R_L 50 Ω

Thévenin Equivalent (seen by R_L)

V_th

8.00 V

R_th

33.3 Ω

I_load

96.0 mA

P_load

0.46 W

The full network and the single-source-plus-resistor equivalent deliver the same current and power to R_L — that identity is the Thévenin theorem, verified live below.

Load Power vs R_L

How it works

The left network is a source V_s with series resistor R1 feeding a node where R2 and the load R_L sit in parallel to ground. Nodal analysis at that node gives:

V_node·(1/R1 + 1/R2 + 1/R_L) = V_s/R1
I_load = V_node / R_L

Thévenin's theorem says that, as far as R_L can tell, everything to its left (V_s, R1, R2) can be replaced by one ideal source V_th in series with one resistor R_th:

V_th = V_s · R2 / (R1 + R2)      (open-circuit voltage, R_L removed)
R_th = R1 ∥ R2 = R1·R2 / (R1 + R2)   (source killed, look into the terminals)
I_load = V_th / (R_th + R_L)

Both formulas give the exact same I_load and load power P_L = I_load²·R_L for any R_L — that's why the two 3D circuits animate identical current flow through their load resistor.

Maximum power transfer: P_L(R_L) = V_th²·R_L / (R_th+R_L)² is maximised exactly when R_L = R_th, giving P_max = V_th² / (4·R_th). The "max power" button snaps the load to that point — drag R_L away from it and watch the power chart fall off on both sides of the peak.

Real-world relevance: this is exactly how engineers size a load (an antenna, a speaker, a sensor) against a source's internal resistance, and why a battery's usable power drops once its own internal resistance is a large fraction of the external load.

R1 · series R2 · parallel branch R_L / R_th · load

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