1. INC 111 Basic Circuit Analysis
Week 2
Kirchoff’s Law

2. Kirchoff’s Current Law (KCL)
“The sum of all currents entering a point is equal zero.” I1 I2 I3 I4
I1 - I2 - I3 + I4 = 0 or
-I1 + I2 + I3 - I4 = 0

3. KCL Metaphor
From the pipe that is full of water, the amount of flow-in water must be equal to the amount of flow-out water.
This is because water cannot disappear.

4. How to use KCL
Place a circle anywhere any size that you want

5. Kirchoff’s Voltage Law
“The sum of all voltages in a closed loop is equal zero.”
+ V2 - + V1 - + V3 -
V1 – V2 – V3 = 0 or -V1 + V2 + V3 = 0

6. KVL Metaphor C
2 m
5 m B
3 m A

7. 4 V
6 V +2 A B
Black = voltage compared to the ground
Red = Voltage difference between 2 points +2 -7
2 V
-1 V C D +3
Close loop
A – B – C – D – A
= 0

8. How to use KVL
Form a loop in the circuit

9. Example: Voltage Divider
X mA
KCL: Current is equal on all points in the circuit because there is no separate path
KVL:

10. Example: Voltage Divider
1mA 0V
10V 4V

11. R in series Equivalent
X mA
X mA

12. Resistor Reduction
Series
(อนุกรม)
Parallel
(ขนาน) or

13. Example
7.5mA 0V
10V
2.5mA
5mA

14. R in parallel Equivalent

15. Voltage & Current Sources Combination

16. Example: Current Divider
1mA 0V
1.333V
0.333mA
0.667mA

17. Voltage Divider

18. Current Divider

19. Example
Find V1

20. Voltmeter and Ammeter
Voltmeter measures the difference of voltage between 2 points.
Put 2 connectors to 2 points that we want to know the voltage difference. V
Ammeter measures the current pass through wire.
Cut the wire, and put the two open-ends to the meter. A

21. Voltmeter V

22. Ammeter A

23. Voltmeter and Ammeter Resistance Characteristic
Same as open circuit ( not connected) A
Same as conductor (wire)

24. Dependent Source The amount of voltage (current) supplied depends on
other voltage (current).
Dependent Voltage Source
Dependent Current Source

25. Example
Find I

26. Example
Find I1

27. KVL on the outer loop