Kirchhoff’s Rules

Kirchhoff’s Current Law (1) KCL: The sum of currents entering any junction in a circuit must equal sum of currents leaving that junction.

Kirchhoff’s Current Law (2) KCL: The sum of currents leaving any junction in a circuit must be zero + If Ii leaves - if Ii enters

Kirchhoff Voltage Law (1)

Kirchhoff Voltage Law (2) KVL: Sum of potential differences across all elements around any closed circuit loop must be zero. + If in the sense of the loop - if against the sense of the loop

Voltage drop between two points The voltage drop between two points is the sum of voltage drops across each element. + If in the sense of the path a  b - if against the sense of the path ab

Steps of Solving a Circuit Problem 1. Straighten out circuit (make squares) 2. Simplify resistors in series/parallel 3. Assign currents, simplify with KCL 4. Write KVL (1 per loop) 5. Solve

Example: Simple Circuit You can simplify resistors in series (but don’t need to) What is current through the bottom battery?