Kirchhoff's Two-Loop Circuit

Two batteries feed a shared resistor. Drag the five sliders and the three branch currents solve live — arrows on the circuit flip direction when a current goes negative. A negative current isn't an error; it's the answer telling you the real direction of flow.

Branch currents I1 + I2 = I3

I1 (left branch)2.00 A

I2 (right branch)1.00 A

I3 (shared R3)3.00 A

Power check delivered = dissipated

P delivered by sources34.0 W

P dissipated in R34.0 W

Balanced to 0.0% — energy is conserved

Battery 2: delivering

EMF ε112.0 V

Resistance R13.0 Ω

EMF ε210.0 V

Resistance R24.0 Ω

Shared R32.0 Ω

Tip: press Show WE-B — battery 2 is now too weak to push, so I2 goes negative and its arrow flips as current is forced backwards through it.