1. Fundamentals of Electric Circuits
Lecture 4
Kirchoff’s Laws

2. RESIRESISTORS IN SERIES RESIRESISTORS IN PARALLEL Voltage Dividers
Kirchoff’s Laws
Circuit Definitions?
Kirchoff’s Current Law (KCL)
Kirchoff’s Voltage Law (KCL)
RESIRESISTORS IN SERIES
RESIRESISTORS IN PARALLEL
Voltage Dividers
Current Dividers

3. Branch – a circuit element between two nodes
Circuit Definitions
Node – any point where 2 or more circuit elements are connected together
Wires usually have negligible resistance
Each node has one voltage (w.r.t. ground)
Branch – a circuit element between two nodes
Loop – a collection of branches that form a closed path returning to the same node without going through any other nodes or branches twice

4. How many nodes, branches & loops?
Example
How many nodes, branches & loops? + - Vs Is R1 R2 R3 Vo

5. Example
Three nodes + - Vs Is R1 R2 R3 Vo

6. Example
5 Branches + - Vs Is R1 R2 R3 Vo

7. Three Loops, if starting at node A
Example
Three Loops, if starting at node A + - Vs Is R1 R2 R3 Vo A B C

8. Kirchhoff’s Current Law THE ALGEBRAIC SUM OF THE CURRENTS
ENTERING A NODE IS ZERO
I = 0 I3 I4 I1 I2 I5
I1 + I2 = I3 + I4 + I5

9. EQUALS CURRENT IN CURRENT OUT ? A 0.5 A - 0.3 A = 0.2 A 0.5 A Example

10. Kirchoff’s Current Law at B+ - Vs Is R1 R2 R3 Vo A B C I2 I1 I3
Assign current variables and directions
Add currents IN, subtract currents OUT: I1 – I2 – I3 + Is = 0

11. Kirchoff’s Current Law
The sum of currents flowing into a node must be equal to sum of currents flowing out of the node. i2 i3
node i1
i1 flows into the node
i2 flows out of the node
i3 flows out of the node
i1 = i2 + i3
i1 – i2 – i3 = 0

12. Kirchoff’s Current Law
Example
Q: How much are the currents i1 and i2 ?
A: i2 = 10 mA – 3 mA = 7 mA
i1 = 10 mA + 4 mA = 14 mA + _ i1
4 mA i2
10 mA
3 mA
node
4 mA + 3 mA + 7 mA = 14 mA

13. Example 1 Determine I, the current flowing out of the voltage source.
Use KCL
1.9 mA mA + I are
entering the node.
3 mA is leaving the node.
V1 is generating power.

14. Kirchhoff’s Current Law
Example: Calculate the unknown currents in the following circuits.

15. Example 2
Suppose the current through R2 was entering the node and the current through R3 was leaving the node.
Use KCL
3 mA mA + I are
entering the node.
1.9 mA is leaving the node.
V1 is dissipating power.

16. Kirchoff’s Voltage Law (KVL)
THE ALGEBRAIC SUM OF VOLTAGES AROUND EACH LOOP IS ZERO
V = 0
E-V1-V2-V3-V4=0

17. Kirchoff’s Voltage Law
v1 = v2 + v3
This equation can also be written in the following form
–v1 + v2 + v3 = 0 + _
+ v2 – v3 – v4 v1
The sum of voltages around a closed loop is zero.

18. Kirchhoff’s Voltage Law
Example :
Calculate the unknown voltages in the given circuit.

19. Example 3
Find the voltage across R1. Note that the polarity of the voltage has been assigned in the circuit schematic.
First, define a loop that include R1.

20. There are three possible loops in this circuit – only two include R1.
Example 3 (con’t)
There are three possible loops in this circuit – only two include R1.
Either loop may be used to determine VR1.

21. If the outer loop is used:
Example 3 (con’t)
If the outer loop is used:
Follow the loop clockwise.

22. Example 3 (con’t) Follow the loop in a clockwise direction.
The 5V drop across V1 is a voltage rise.
VR1 should be treated as a voltage rise.
The loop enters R2 on the positive side of the voltage drop and exits out the negative side. This is a voltage drop as the voltage becomes less positive as you move through the component.

23. Example 3 (con’t)
By convention, voltage drops are added and voltage rises are subtracted in KVL.

24. Kirchhoff’s Voltage Law