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Express the equivalent resistance of the combination of R3, R4, R5 and R6. 

To determine the equivalent resistance of the combination of resistors \( R_3 \), \( R_4 \), \( R_5 \), and \( R_6 \), we need to analyze how these resistors are connected. 

From the image:

1. **Parallel Combination**:
   - \( R_4 \) and \( R_5 \) are connected in series, which we can combine first:
     \[
     R_{45} = R_4 + R_5
     \]
   - \( R_{45} \) is then connected in parallel with \( R_6 \):
     \[
     R_{456} = \left(\frac{1}{R_{45}} + \frac{1}{R_6}\right)^{-1} = \left(\frac{1}{R_4 + R_5} + \frac{1}{R_6}\right)^{-1}
     \]
   - Now, \( R_3 \) is connected in series with \( R_{456} \):
     \[
     R_{3456} = R_3 + R_{456}
     \]
   - Thus, the equivalent resistance of the combination of \( R_3 \), \( R_4 \), \( R_5 \), and \( R_6 \) is given by:
     \[
     R_{\text{eq}} = R_3 + \left(\frac{1}{R_4 + R_5} + \frac{1}{R_6}\right)^{-1}
     \]

Would you like more details on any specific part of this process?

Here are five related questions to deepen your understanding:

1. How does the series connection of resistors differ from a parallel connection in terms of equivalent resistance?
2. If one of the resistors \( R_4 \) or \( R_5 \) were removed, how would that affect the equivalent resistance?
3. Can you calculate the equivalent resistance if specific values for \( R_3 \), \( R_4 \), \( R_5 \), and \( R_6 \) were given?
4. What are the implications of high versus low resistance in a circuit?
5. How does the equivalent resistance of a circuit impact the total current flowing through it?

**Tip:** Always remember to simplify resistor networks step by step, combining series and parallel connections progressively to find the overall equivalent resistance.

Learn how to calculate the equivalent resistance of a combination involving resistors R3, R4, R5, and R6. This problem covers series and parallel circuits, parallel and series resistance formulas, and their application in electrical circuit analysis. Suitable for advanced high school students and beyond.

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