Polytechnic · Engineering Round 1/6 Score 0

🔧 Kirchhoff Junction

Balance two loops, then solve their Thévenin equivalent.

Balance the junction

Make every residual zero.
KCL residual0 A
Left-loop KVL residual0 V
Right-loop KVL residual0 V
I₁ I₂ I₃ I₁ + I₂ = I₃
KCL conserves charge at a junction; KVL conserves energy round a loop.

Set branch currents

Live load-power curve

The physics

KCL: ΣI_entering = ΣI_leaving (A).

KVL: Σ voltage rises − Σ voltage drops = 0 V.

Ohm's law: V = IR. The branch current sign indicates its direction.

Thévenin: Vth = (E₁/R₁ + E₂/R₂)/(1/R₁ + 1/R₂).

With ideal sources set to zero, Rth = R₁R₂/(R₁ + R₂).

Load power: P = Vth²RL/(Rth + RL)². Its maximum occurs at RL = Rth.