Basic Electrical Engineering - GEC 210

Basic Electrical Engineering - GEC 210

• Course instructor: Asia'u Talatu Belgore
• Email: asia'[email protected]
• Office: D25

Circuit/Network Analysis

• Two general approaches exist:
  • Direct Method: Analyzes the network in its original form, determining voltages and currents. Primarily used for simple circuits
  • Network Reduction Method: Converts the original network to a simpler equivalent circuit for quicker quantity calculations. Applicable to both simple and complex networks. Examples include Delta/Star and Star/Delta conversions, Thevenin's theorem, and Norton's theorem.

Source Transformation

• An equivalent circuit has identical voltage-current characteristics to the original circuit.
• Two types of sources exist:
  • Voltage sources: Value is fixed or is dependent on the voltage/current elsewhere in the circuit
  • Current sources: Value is fixed or is dependent on the voltage/current elsewhere in the circuit
• Source transformation: Replaces a voltage source in series with a resistor with a current source in parallel with the same resistor, or vice versa. Vs = Is x R

Mesh Analysis

• Used for analyzing circuits using mesh currents.

• Steps:

  • Obtain the number of meshes (m)
  • Assign mesh currents (i₁, i₂, ..., iₘ) – clockwise is common.
  • Define voltage drop polarities based on the mesh direction.
  • Apply KVL to each mesh, expressing voltages in terms of mesh currents.
  • Solve the simultaneous equations to determine the unknown mesh currents.

• A circuit with fewer nodes than meshes is best analyzed using nodal analysis. Conversely, a circuit with fewer meshes than nodes is better analyzed using mesh analysis.

Nodal Analysis

• Used for analyzing circuits using node voltages.

• Steps:

  • Obtain the number of nodes (n)
  • Select a node as the reference (often ground, V₀ = 0V).
  • Assign voltages to remaining nodes (V₁, V₂, ..., Vₙ₋₁).
  • Apply KCL to each non-reference node; use Ohm's law to express branch currents in terms of node voltages.
  • Solve the simultaneous equations to determine the unknown node voltages.

• Current flows from a high potential to a low potential in a resistor.

• If a voltage source connects the reference node and a non-reference node, the non-reference node voltage is the same as the voltage source.

Steps (for calculating junction potentials)

• Identify principle nodes/junctions in the circuit
• Assign junction potentials relative to the reference junction (VO = 0V)
• Assuming all currents are outgoing for KCL
• Solve equations to find junction potentials.

Star and Delta Connections

• Useful for simplifying complex networks with multiple interconnected resistors

• Simplifies by interchanging connected resistor configurations to a more manageable form

• Uses formulas such as:

  • Rₐb = (RₐRₓ + RₓR♭ + R♭Rₐ)/Rₓ
  • Rbc = (RₐRₓ+RₓR♭+ R♭Rₐ)/Rₐ
  • Rca = (RₐRₓ+RₓR♭+ R♭Rₐ)/R♭

• Identical Resistances: Simplified formulas exist for situations involving identical resistances.

Network Theorems

• Superposition theorem: Multiple sources' effects can be calculated individually, and then combined algebraically to find the total current in any component of the network.
• Thevenin's theorem: Replaces complex multiple-source networks with a simple equivalent circuit consisting of a single voltage source and a single resistor.
• Norton's theorem: Replaces complex networks with an equivalent circuit having a constant current source in parallel with a resistor

This quiz covers Circuit/Network Analysis and Source Transformation as part of the Basic Electrical Engineering course. Students will explore methods such as Direct Method and Network Reduction, along with concepts related to voltage and current sources. Prepare to test your understanding of key theories and applications.