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Source transformation is the technique of swapping a voltage source in series with a resistor for an equivalent current source in parallel with the same-valued resistor (or vice versa), without changing how the rest of the circuit behaves. It is exactly the Thevenin↔Norton relationship applied as a circuit-simplification tool: repeatedly transforming and combining sources lets you collapse a multi-source network down to a single equivalent source before analyzing the load, often avoiding a full mesh/nodal solution.
| Direction | Formula |
|---|---|
| Voltage → Current source | Is = Vs/Rs, Rp = Rs |
| Current → Voltage source | Vs = Is×Rp, Rs = Rp |
The two forms are only equivalent as seen from the external terminals — internal power dissipation in the resistor can differ from the original physical source, so use source transformation for terminal-behavior analysis, not for finding power lost inside a real component.
A technique that converts a voltage source with a series resistor into an equivalent current source with a parallel resistor (or vice versa), preserving the same voltage-current behavior at the two external terminals.
Is = Vs/Rs, with the resistance staying the same value but moving from series to parallel: Rp = Rs.
Vs = Is×Rp, with the resistance moving from parallel to series: Rs = Rp.
It is the same underlying relationship — a Thevenin equivalent (Vth, Rth) and its Norton equivalent (IN, RN) are related by exactly the source transformation formulas.
It lets you combine multiple sources and resistors that are not directly in series or parallel, often reducing a multi-source network to one equivalent source without setting up mesh or nodal equations.
Yes — you can transform several sources to the same form (all current sources, for example), combine them in parallel, then transform the combined result back if a voltage-source view is more convenient.
No — only the external terminal behavior (V-I relationship as seen by the rest of the circuit) is preserved. Internal dissipation in the transformed resistor is generally not the same as in the original physical component.
No — with Rs=0 the equivalent current would be infinite, so an ideal voltage source has no current-source equivalent. Likewise, an ideal current source (Rp=∞) has no voltage-source equivalent.
Yes, source transformation applies equally to dependent (controlled) sources as long as the controlling variable is kept in the circuit and not eliminated during the transformation.
Yes, using impedances instead of resistances: Is=Vs/Zs and Zp=Zs, both generally complex at a given frequency.
No — superposition analyzes each source's individual contribution with others deactivated; source transformation converts and combines sources into fewer equivalent elements. They are complementary techniques.
Add the current sources algebraically (accounting for direction) and combine their parallel resistances using the standard parallel-resistor formula, then optionally convert the combined result back to a voltage source.
Because the transformation is derived directly from Ohm's law equivalence at the terminals; the physical resistance value does not change, only its circuit position (series vs. parallel) relative to the source.
Yes, transforming voltage→current→voltage (or the reverse) returns the exact original values, since both formulas are algebraic inverses of each other.
Thevenin Equivalent Circuit • Norton Equivalent Circuit • Millman's Theorem • All Calculators