The Thévenin equivalent circuit is derived from the Norton equivalent circuit as shown below. Given IN = 5 A, RN = 39 2, calculate the value of the Thévenin equivalent resistance Rth in ohms to one decimal place.

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**Title: Calculating Thévenin Equivalent Resistance from a Norton Equivalent Circuit**

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**Introduction:**

The process of deriving a Thévenin equivalent circuit from a Norton equivalent circuit is an essential concept in electrical engineering. It aids in simplifying complex circuits for easier analysis.

**Problem Statement:**

Given the Norton equivalent circuit parameters:
- Norton current, \( I_N = 5 \, \text{A} \)
- Norton resistance, \( R_N = 39 \, \Omega \)

Calculate the Thévenin equivalent resistance \( R_{Th} \) in ohms accurate to one decimal place.

**Circuit Explanation:**

*Diagram Description*:

1. **Norton Equivalent Circuit:**

   - A current source \( I_N \) of 5 A is depicted on the left.
   - The current source is in parallel with a resistor \( R_N \) of 39 Ω.
   - Two nodes are marked as a and b, defining the points for which the equivalent is to be found.

2. **Thévenin Equivalent Circuit:**

   - On the right, the circuit reduces to a voltage source \( V_{Th} \) in series with a resistor \( R_{Th} \), connected between the same nodes a and b.

**Solution:**

Since \( R_{Th} = R_N \) for conversion purposes (Thévenin and Norton resistances are equal), the Thévenin equivalent resistance \( R_{Th} \) is:

\[ R_{Th} = 39.0 \, \Omega \]

This simplified calculation helps in further analysis or integration of the circuit into larger systems.

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**Conclusion:**

By understanding these conversions, engineers can model electrical networks with greater flexibility and accuracy, enhancing problem-solving efficiency.
Transcribed Image Text:**Title: Calculating Thévenin Equivalent Resistance from a Norton Equivalent Circuit** --- **Introduction:** The process of deriving a Thévenin equivalent circuit from a Norton equivalent circuit is an essential concept in electrical engineering. It aids in simplifying complex circuits for easier analysis. **Problem Statement:** Given the Norton equivalent circuit parameters: - Norton current, \( I_N = 5 \, \text{A} \) - Norton resistance, \( R_N = 39 \, \Omega \) Calculate the Thévenin equivalent resistance \( R_{Th} \) in ohms accurate to one decimal place. **Circuit Explanation:** *Diagram Description*: 1. **Norton Equivalent Circuit:** - A current source \( I_N \) of 5 A is depicted on the left. - The current source is in parallel with a resistor \( R_N \) of 39 Ω. - Two nodes are marked as a and b, defining the points for which the equivalent is to be found. 2. **Thévenin Equivalent Circuit:** - On the right, the circuit reduces to a voltage source \( V_{Th} \) in series with a resistor \( R_{Th} \), connected between the same nodes a and b. **Solution:** Since \( R_{Th} = R_N \) for conversion purposes (Thévenin and Norton resistances are equal), the Thévenin equivalent resistance \( R_{Th} \) is: \[ R_{Th} = 39.0 \, \Omega \] This simplified calculation helps in further analysis or integration of the circuit into larger systems. --- **Conclusion:** By understanding these conversions, engineers can model electrical networks with greater flexibility and accuracy, enhancing problem-solving efficiency.
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