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The circuit shown consists of multiple resistors, with the given resistances:

- \( R_1 = R_2 = R_3 = 2.29 \, \Omega \)
- \( R_4 = 17.2 \, \Omega \)
- \( R_5 = 7.03 \, \Omega \)
- \( R_6 = 3.72 \, \Omega \)

Additionally, the current through \( R_6 \) is given as \( i_6 = 1.37 \, \text{A} \). We need to find the electromotive force (emf) \( \mathcal{E} \) of the ideal battery.

### Steps to Solve:
1. **Calculate the voltage across \( R_6 \)** using Ohm's law:
   \[
   V_6 = i_6 \cdot R_6 = 1.37 \, \text{A} \cdot 3.72 \, \Omega = 5.0964 \, \text{V}
   \]

2. **Determine the equivalent resistance for the parallel combination of \( R_5 \) and \( R_6 \)**:
   \[
   \frac{1}{R_{56}} = \frac{1}{R_5} + \frac{1}{R_6} = \frac{1}{7.03} + \frac{1}{3.72}
   \]
   Solving this gives:
   \[
   R_{56} \approx 2.415 \, \Omega
   \]

3. **Find the total resistance of the series combination** of \( R_4 \) and \( R_{56} \):
   \[
   R_{\text{total}} = R_4 + R_{56} = 17.2 \, \Omega + 2.415 \, \Omega = 19.615 \, \Omega
   \]

4. **Now, analyze the overall circuit**, which is a combination of the series resistors \( R_1 \), \( R_2 \), and the equivalent resistance of the right-hand portion (\( R_4 + R_{56} \)).

   The total equivalent resistance \( R_{\text{eq}} \) of the entire circuit is:
   \[
   R_{\text{eq}} = R_1 + R_2 + R_3 + R_{\text{total}} = 2.29 \, \Omega + 2.29 \, \Omega + 2.29 \, \Omega + 19.615 \, \Omega = 26.485 \, \Omega
   \]

5. **Using Ohm’s law**, the emf of the battery \( \mathcal{E} \) is calculated as:
   \[
   \mathcal{E} = i_6 \cdot R_{\text{eq}} = 1.37 \, \text{A} \cdot 26.485 \, \Omega \approx 36.29 \, \text{V}
   \]

Thus, the emf of the ideal battery is approximately **36.29 V**.

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Would you like more details on any part of the calculation? 

Here are some related questions to expand your understanding:
1. What is the role of parallel and series resistances in a circuit?
2. How does the current split in parallel circuits?
3. Why is the equivalent resistance lower in parallel circuits?
4. How does Ohm’s law relate voltage, current, and resistance?
5. How can we determine power consumption in this circuit?

**Tip:** For complex circuits, breaking them down into simpler series and parallel combinations makes calculations easier!

In the figure, the current in resistance 6 is i6 = 1.37 A and the resistances are R1 = R2 = R3 = 2.29 Ω, R4 = 17.2 Ω, R5 = 7.03 Ω, and R6 = 3.72 Ω. What is the emf of the ideal battery?

Learn how to calculate the EMF of a battery in a circuit involving series and parallel resistors. Using Ohm's law, series, and parallel resistance formulas, this problem shows step-by-step calculations for resistances R1 = 2.29 Ω to R6 = 3.72 Ω. Suitable for advanced high school or college-level students.

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