1. Lecture 3 Review: Kirchoff’s Current Law Kirchoff’s Voltage Law
Ohm’s Law, Power, Power Conservation
Kirchoff’s Current Law
Kirchoff’s Voltage Law
Related educational materials:
Chapter 1.4

2. Review: Ohm’s Law Ohm’s Law Voltage-current characteristic
of ideal resistor:

3. Review: Power
Power:
Power is positive if i, v agree with passive sign convention (power absorbed)
Power is negative if i, v contrary to passive sign convention (power generated)

4. Review: Conservation of energy
Power conservation:
In an electrical circuit, the power generated is the same as the power absorbed.
Power absorbed is positive and power generated is negative

5. Two new laws today: Kirchoff’s Current Law Kirchoff’s Voltage Law
These will be defined in terms of nodes and loops

6. Basic Definition – Node
A Node is a point of connection between two or more circuit elements
Nodes can be “spread out” by perfect conductors

7. Basic Definition – Loop
A Loop is any closed path through the circuit which encounters no node more than once

8. Kirchoff’s Current Law (KCL)
The algebraic sum of all currents entering (or leaving) a node is zero
Equivalently: The sum of the currents entering a node equals the sum of the currents leaving a node
Mathematically:
We can’t accumulate
charge at a node

9. Kirchoff’s Current Law – continued
When applying KCL, the current directions (entering or leaving a node) are based on the assumed directions of the currents
Also need to decide whether currents entering the node are positive or negative; this dictates the sign of the currents leaving the node
As long all assumptions are consistent, the final result will reflect the actual current directions in the circuit

10. KCL – Example 1
Write KCL at the node below:

11. KCL – Example 2
Use KCL to determine the current i

12. Kirchoff’s Voltage Law (KVL)
The algebraic sum of all voltage differences around any closed loop is zero
Equivalently: The sum of the voltage rises around a closed loop is equal to the sum of the voltage drops around the loop
Mathematically:
If we traverse a loop, we end up
at the same voltage we started with

13. Kirchoff’s Voltage Law – continued
Voltage polarities are based on assumed polarities
If assumptions are consistent, the final results will reflect the actual polarities
To ensure consistency, I recommend:
Indicate assumed polarities on circuit diagram
Indicate loop and direction we are traversing loop
Follow the loop and sum the voltage differences:
If encounter a “+” first, treat the difference as positive
If encounter a “-” first, treat the difference as negative

14. KVL – Example
Apply KVL to the three loops in the circuit below. Use the provided assumed voltage polarities

15. Circuit analysis – applying KVL and KCL
In circuit analysis, we generally need to determine voltages and/or currents in one or more elements
We can determine voltages, currents in all elements by:
Writing a voltage-current relation for each element (Ohm’s law, for resistors)
Applying KVL around all but one loop in the circuit
Applying KCL at all but one node in the circuit

16. Circuit Analysis – Example 1
For the circuit below, determine the power absorbed by each resistor and the power generated by the source. Use conservation of energy to check your results.

17. Example 1 – continued

18. Circuit Analysis – Example 2
For the circuit below, write equations to determine the current through the 2 resistor

19. Example 2 – Alternate approach

20. Circuit Analysis
The above circuit analysis approach (defining all “N” unknown circuit parameters and writing N equations in N unknowns) is called the exhaustive method
We are often interested in some subset of the possible circuit parameters
We can often write and solve fewer equations in order to determine the desired parameters

21. Circuit analysis – Example 3
For the circuit below, determine:
(a) The current through the 2 resistor
(b) The current through the 1 resistor
(c) The power (absorbed or generated) by the source

22. Circuit Analysis Example 3 – continued