4.4: Dependent Sources

INDEPENDENT VS. DEPENDENT SOURCES

1. INDEPENDENT SOURCES

a) Independent voltage source:

Two terminal element that maintains a specified voltage between its terminal.

b) Independent current source:

Two terminal element that maintains a specified current between its terminal.

2. DEPENDENT SOURCES

Generate voltage or current based on the voltage or current at some specified location in the circuit. It divides into four types:

a) Voltage controlled voltage source: V = uVx

b) Current-controlled voltage source: V = R(ohms)Ix

c) Voltage-controlled current source: I = G (1/ohm)Vs

d) Current-controlled current source: I = BIx

Example:
Find Vo in the circuit below

4.2: Source Transformation

SOURCE TRANSFORMATION

Process of replacing a voltage sources and current sources as follows:
1. Replace voltage source (Vs) in series with a resistor (Rs) by a current source (Is).
2. Replace current source (Is) in parallel with resistor (Rs) by a voltage source (Vs)
3. Two or more parallel current sources can be summed and represented as one current source.
4. Two or more series voltage sources can be summed and replaced with one voltage source.

Example:
For the circuit below use source conversion to simplify the circuit as much as possible and calculate RL that results in maximum power transfer.

4.1: Superposition

SUPERPOSITION

Rules to follow:

1. Turn off all independent source but one, and find voltages/current in the circuit due to the one active source.

• Voltage off = replace with a short
• Current off = replace with an open

2. Repeat step 1 for each source

3. For desired voltage/current, you simple sum each independent contribution.

Example:

Find Vo in the circuit below:

2.1: Basic Laws

NETWORK TERMINOLOGY

1. Branches: single elements and its terminals.
2. Nodes: Points of connection between one or more branches/elements
3. Loop: Closed path in which each element is visited once.
4. Mesh: Loop without any other loops inside it.

OHM'S LAW

Voltage V across the resistor is directly proportional to the current going through it.

V = IR

[Volts] = [Amps][Ohms]

• CASE I: Short circuit

If resistance = 0, voltage = 0

• CASE II: Open circuit

If resistance = infinitive, current = 0

KIRCHOFF'S LAWS

1. Kirchoff's current law (KCL): The alebraic sum of currents entering a node (or closed boundary) is zero.

Example:
In the circuit below, determine I1 and I2

By adding the current at each node we have:

I1 = 8mA + 4mA = 12mA

I2 = 8mA - 2mA = 6mA

1.1: Definitions

ELECTRICAL CIRCUIT: Interconnection of electrical elements and symbols. They divide into:

a) Passive: Cannot generate energy

• Resistor (R) - [Ohms]
• Capacitor (C) - [Farads]
• Inductor (L) - [Henries]

b) Active: May or may not generate/supply energy

• Voltage (V) - [Volts]
• Current (I) - [Amps]

Important definitions in circuits go as follows:

4.5: Concentration of Solutions

MOLARITY

Example 1:
What's the molarity of 5.00g C6H12O6 if you were to make 100 mL solution?

3.2: Mesh Analysis

MESH ANALYSIS

Can only be applied to planar circuits.

STEPS:

1. Assign mesh currents.

2. Apply KVL to each mesh.

• CASE I: Current source in 1 mesh (Ia = i1)
• CASE II: Current source in 2 meshes (Called supermesh where Ia = i1 - i2)

3. Solve.