Kirchhoff's Rules

Kirchhoff’s Voltage Rules

• Stats that the sum of the $\Delta V$ (voltage drops) caused by anything around a loop must be zero

  • why?? because the potential defference between them is

Kichhoff’s Current Rule

• Statse that the sum of the currents entering any given point in a circuit must equal the sum of all currens leaving the same point

• Ex

  • 
    • $I_1+I_2=I_3$ because the currents is flowing around and coming back to the junction at a

How to solve

• 1. Label each current (including its direction)

• 2. Chose nodes and loops

• 3. Apply node and loop rules; you will need as many independent equations as unknowns (we can just make them for free)

  • If we have N loops, only N-1 are independent

Examples

• 1. Calculate the currents $I_1,I_2,I_3$ in the three branches of the circuit

  • 
    • for each node we know that $I_{in}=I_{out}$
      • we can compare A and D
      • A: $I_3=I_1+I_2$
      • D: $I_1+I_2=I_3$
        • they are not independent because they are the same equation lol
    • And we know that the $\sum V=0$
      • and to solve we must isolate each loop (giving us an equastion each (V=IR for the entire guy =0))

    • Upper;

      • $30I_1-45+1I_3+40I_3=0$

    • Lower:

      • $-80+1I_2+20I_2-45+40I_3=0$