Kirchhoff's Circuit Laws

Electric charge can't pile up or vanish, so at any junction the current flowing in must exactly equal the current flowing out. Energy can't appear or disappear either, so if you add up all the voltage gains and drops all the way around any closed loop, they cancel to zero.

ΣI_in = ΣI_out ; ΣΔV = 0

  • I_in — current in (A): total current flowing into a junction
  • I_out — current out (A): total current flowing out of that same junction
  • ΔV — voltage change (V): a gain or drop in voltage across one part of a loop

A wire carries 6 A into a junction, where it splits into two branches. One branch carries 4 A. How much current flows through the other branch?

  • I_in = 6 A
  • I_out1 = 4 A
  1. I_out2 = I_in − I_out1
  2. I_out2 = 6 A − 4 A

I_out2 = 2 A

A junction now has 9 A flowing in, splitting into two branches. One branch carries 5 A. What flows through the other branch?

  • 4 A
  • 14 A
  • 5 A

Going all the way around a closed loop in a circuit, adding up every voltage rise and drop, what must the total equal?

  • The total current
  • Zero
  • The battery's voltage doubled