source transformation

source transformation

1. What Source Transformation Is

Source transformation = technique to replace a voltage source $V_s$ in series with $R_s$ by an equivalent current source $I_s = V_s/R_s$ in parallel with same $R_s$ (now $R_p = R_s$), and vice versa, without changing external circuit behaviour (same $V$–$I$ at terminals). Used to simplify circuits for mesh/nodal analysis.

2. Equivalence Conditions

• Voltage → Current:

(current source in parallel with $R_s$).

• Current → Voltage:

(voltage source in series with $R_p$).

Must keep same $R$ value and same polarity/direction: positive terminal of $V_s$ corresponds to arrow head of $I_s$ pointing away from that terminal (see diagram).

Valid only for external load, not internal power: power dissipated in $R_s$ differs, but terminal behaviour same.

Complex circuit with many sources: transform all voltage sources to current sources (or vice versa) to get single equivalent source + resistor, then compute.

Example: Two voltage sources with series Rs: transform both to current sources in parallel → combine I_eq = I1+I2, Rp = Rp1||Rp2 → transform back to single voltage source if needed for load calculation.

5. Exam Points

• State transformation $V_s↔I_s=V_s/R_s$, $R_s↔R_p$ same — 5 marks, very frequent (almost certain to ask with diagram).
• Show direction correspondence — 3 marks, frequent.
• Solve circuit by transforming voltage to current and back — 7-10 marks, very frequent (common simplification numerical).
• Mention valid for external load only — 3 marks.