Kirchhoff’s Rules

321 III

Kirchhoff’s Current Law (1)

KCL: The sum of currents entering any junction in a circuit must equal sum of currents leaving that junction.

0132 III

Kirchhoff’s Current Law (2)KCL: The sum of currents leaving any junction in a circuit must be zero

01

N

iiI

+ If Ii leaves

- if Ii enters

0path closed V

Kirchhoff Voltage Law (1)

IRIr

Kirchhoff Voltage Law (2)KVL: Sum of potential differences across all elements around any closed circuit loop must be zero.

0 IRIr

011

N

ii

N

iiiRI

+ If in the sense of the loop

- if against the sense of the loop

Voltage drop between two pointsThe voltage drop between two points is the sum of voltage drops across each element.

IrVV ba

N

ii

N

iiiba RIVV

11

+ If in the sense of the path a b

- if against the sense of the path ab

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?