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To calculate the Thevenin resistance \( R_{Th} \) for the network given between points **a** and **b**, we'll follow these steps:

1. **Turn off all independent sources**: 
   - The 20V voltage source will be replaced by a short circuit.
   - The 6A current source will be replaced by an open circuit.

2. **Simplify the resulting circuit**: 
   After deactivating the sources, the 5Ω and 20Ω resistors will remain, along with the 3Ω resistor between points a and b. We can now calculate the equivalent resistance seen between points a and b.

### Step-by-step calculation:

- The 5Ω and 20Ω resistors are in parallel, so their equivalent resistance \( R_{eq1} \) is:
  \[
  R_{eq1} = \frac{(5 \times 20)}{(5 + 20)} = \frac{100}{25} = 4\ \Omega
  \]
- Now, this 4Ω equivalent resistance is in series with the 3Ω resistor between points a and b, giving the total Thevenin resistance \( R_{Th} \):
  \[
  R_{Th} = 4\ \Omega + 3\ \Omega = 7\ \Omega
  \]

### Conclusion:
The Thevenin resistance \( R_{Th} \) between points **a** and **b** is \( \mathbf{7\ \Omega} \).

Would you like more details or have any questions? 

Here are some related questions:
1. How would the calculation change if there were additional resistors between points a and b?
2. What would happen if the current source were kept active while calculating \( R_{Th} \)?
3. How would you calculate the open-circuit voltage \( V_{Th} \) in this circuit?
4. Can we apply the same method to a circuit with dependent sources? How?
5. What happens if we swap the 20Ω resistor with an inductor? How does that affect the time-domain response?

**Tip**: When deactivating sources, always remember to short-circuit voltage sources and open-circuit current sources.

Calculate R_Th for the network given between a and b.

Step-by-step solution to calculate the Thevenin resistance (R_Th) between points a and b in a circuit with independent voltage and current sources. Learn to deactivate sources and apply series-parallel resistance rules. Ideal for undergraduate engineering students or advanced high school learners.

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