1. Lecture 2 - Circuit Elements and Essential Laws
E E 1205 Circuit Analysis
Lecture 2 - Circuit Elements and Essential Laws

2. Five Fundamental Elements
Ideal Voltage Sources
Independent
Dependent
Ideal Current Sources
Resistors
Inductors (to be introduced later)
Capacitors (to be introduced later)

3. Independent Voltage Source
Voltage may be constant or time-dependent
Delivers nominal terminal voltage under all conditions

4. Independent Current Source
Current may be constant or time-dependent
Delivers nominal terminal current under all conditions

5. Voltage-Controlled Dependent Voltage Source
Terminal voltage is a function of the voltage drop of a different branch
Delivers nominal terminal voltage under all conditions

6. Current-Controlled Dependent Voltage Source
Terminal voltage is a function of the current flow in a different branch
Delivers nominal terminal voltage under all conditions

7. Voltage-Controlled Dependent Current Source
Current is a function of the voltage drop of a different branch
Delivers nominal terminal current under all conditions

8. Current-Controlled Dependent Current Source
Source current is a function of the current flow in a different branch
Delivers nominal terminal current under all conditions

9. Electrical Resistance (Ohm’s Law)
Electrical resistance is the ratio of voltage drop across a resistor to current flow through the resistor.
Polarities are governed by the passive sign convention.

10. Power Consumed by Resistors
Resistors consume power.
v and i are both positive or both negative.

11. Conductance Defined Conductance is the reciprocal of resistance.
The units of conductance are called siemens (S)
The circuit symbol is G

12. Creating a Circuit Model
A circuit model is usually two or more circuit elements that are connected.
A circuit model may have active elements (sources) as well as passive elements (such as resistors).
By the assumption that electric signal propagation is instantaneous in a circuit, our circuit model has lumped parameters.

13. Example of a Circuit Model

14. Kirchhoff’s Voltage Law
The sum of the voltage drops around a closed path is zero.
Example: V1 + V2 + V3 + V4 = 0

15. Kirchhoff’s Current Law
A node is a point where two or more circuit elements are connected together.
The sum of the currents leaving a node is zero.

16. Apply KCL to Example

17. Combine KVL, KCL & Ohm’s Law

18. Lamp Voltage & Battery Voltage

19. Battery Power and Lamp Power
Loss:
Efficiency:

20. Using Loops to Write Equationsa:
Loop b:
Loop c:
Loop c equation same as a & b combined.

21. Using Nodes to Write Equations
Node x:
Node y:
Node z:
Node w:
<== Redundant

22. Combining the Equations
There are 5 circuit elements in the problem.
va and vb are known.
R1, R2 and R3 are known.
v1, v2 and v3 are unknowns.
ia, ib, i1, i2 and i3 are unknowns.
There are 2 loop (KVL) equations.
There are 3 node (KCL) equations.
There are 3 Ohm’s Law equations.
There are 8 unknowns and 8 equations.

23. Working with Dependent Sources
left loop:
top right node:
Substitute and solve:

24. Example 1 (1/3)
By KCL:
By Ohm’s Law:

25. Example 1 (2/3)
By KVL:
Power:

26. Example 1 (3/3)

27. Example 2 (1/4)
Find Source Current, I, and Resistance, R.

28. Example 2 (2/4)
Ohm’s Law: 36 V
KVL: 48 V
Ohm’s Law: 6 A

29. Example 2 (3/4)
KCL: 3 A
Ohm’s Law: 12 V
KVL: 60 V

30. Example 2 (4/4) Ohm’s Law: 3 A KCL: 6 A KVL: 24 V Ohm’s Law: R=3 W
KCL: I=9 A