TR3.5

Kirkoff's Laws

Houjun Liu 2021-09-27 Mon 12:00

1 Kirkoff's Laws

1.1 Kirkoff's First Law

\definition{Kirkoff's First Law}{**Sum of voltage in any closed loop should add up to 0**} As in, the sum of all voltage changes from Start => Start will add up to 0.

1.2 Kirkoff's Second law

\definition{Kirkoff's Second Law}{**Net current flowing into a node is 0**} With a current \(i_0\), when it flows into a junction like B, the current \(i_0\) splits into \(i_2\) and \(i_3\)

1.3 A Quick Kirkoff Excercise

Here's a circuit:

Screen Shot 2020-09-14 at 10.38.44 AM.png

Figure 1: Screen Shot 2020-09-14 at 10.38.44 AM.png

So, to calculate the resistance and current at every point o

START at start

  • \(+12\)
  • \(-I_1*10\) (per \(I = \frac{\Delta V}{resistance}\))
  • \(-I_2 * 20\)
  • \(-I_1 * 15\)
  • \(= 0\)

\(I_1 - I_2 - I_3 = 0\), per Kirerbab's Second Law.