Lecture Notes: Norton's Theorem and Current Calculation

Overview

• Topic: Using Norton’s theorem to calculate the current flowing through a load resistor.
• Objective: Calculate Norton’s resistance and current, draw the equivalent circuit, and determine the current through the load resistor (IL).

Key Steps and Concepts

1. Calculate Norton's Resistance

• Norton's resistance (Rn) is the same as Thevenin's resistance (Rth).
• Replace independent voltage source with a short circuit and independent current source with an open circuit.
• Disconnect the load resistor.
• Find equivalent resistance across points A and B.

Example Values Update

• Correct the 5 ohm resistor to 8 ohms.
• Resistors: 8Ω, 3Ω, and another 3Ω.
• Series: 8Ω + 3Ω = 11Ω.
• Parallel: 1/11 + 1/3 = 2.357Ω (Norton's resistance).

2. Calculate Norton's Current

• Disconnect the load resistor (RL = 6Ω initially).
• Open terminal across the 3Ω resistor. Points: B, A, C.
• Use nodal analysis at point C (Kirchhoff's Current Law).
• Define currents: I1, I2 (7A), and I3.
• Solve for VC (Electric potential at point C).

Nodal Analysis Equations

• I1 = (100 - VC) / 8
• I2 = 7A
• I3 = VC / 3
• Equation: (100 - VC) / 8 + 7 - VC / 3 = 0.
• Solve for VC: 66.857V.

3. Calculate Thevenin Voltage

• Use voltage divider: VA = VC * (R3 / (R2 + R3)).
• Calculate VA (Thevenin voltage): 33.4285V.*

4. Calculate Norton’s Current (In)

• In = VA / Rn = 33.4285 / 2.357 = 14.183A.

5. Determine Load Resistor Current (IL)

• Use current divider: IL = In * (Rn / (Rn + RL)).
• Calculation: 14.183 * (2.357 / 8.357) = 4A.

Verification

• Validate through potential difference and current consistency.
• Ensure all calculated values align with initial problems’ constraints.