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To solve this problem, let's analyze the circuit given.

### Given Data
- The current source \( I_s = 10 \, \text{A} \).
- There are resistors with values of \(1 \, \Omega\) each.

### Step-by-Step Solution
1. **Identify the Branches of the Circuit**:
   - The circuit appears to have three resistors in series along the path labeled with current \( I \).
   - The left side has a current source \( I_s = 10 \, \text{A} \), and it’s in parallel with a branch of three \( 1 \, \Omega \) resistors.

2. **Calculate the Total Resistance in Each Branch**:
   - In the left branch, where \( I_s = 10 \, \text{A} \) flows, there’s a single \(1 \, \Omega\) resistor.
   - In the branch where current \( I \) flows, we have three resistors in series:
     \[
     R_{\text{total in right branch}} = 1 \, \Omega + 1 \, \Omega + 1 \, \Omega = 3 \, \Omega
     \]

3. **Determine the Equivalent Resistance**:
   - Since the two branches are in parallel, the equivalent resistance \( R_{\text{eq}} \) can be found using the parallel resistance formula:
     \[
     \frac{1}{R_{\text{eq}}} = \frac{1}{1 \, \Omega} + \frac{1}{3 \, \Omega} = \frac{3 + 1}{3} = \frac{4}{3}
     \]
     \[
     R_{\text{eq}} = \frac{3}{4} \, \Omega
     \]

4. **Calculate the Voltage Across Each Branch**:
   - The total current \( I_s = 10 \, \text{A} \) flows through the equivalent resistance \( R_{\text{eq}} \), so the total voltage \( V \) across each branch is:
     \[
     V = I_s \times R_{\text{eq}} = 10 \, \text{A} \times \frac{3}{4} \, \Omega = 7.5 \, \text{V}
     \]

5. **Calculate the Labeled Current \( I \) in the Right Branch**:
   - Using Ohm’s law, the current \( I \) in the right branch (with resistance \( 3 \, \Omega \)) is:
     \[
     I = \frac{V}{R_{\text{total in right branch}}} = \frac{7.5 \, \text{V}}{3 \, \Omega} = 2.5 \, \text{A}
     \]

### Answer
The labeled current \( I \) is:
\[
I = 2.5 \, \text{A}
\]

Would you like further details on any step, or do you have any questions?

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### Related Questions
1. How would the current \( I \) change if the resistor values in the right branch were different?
2. What would happen to \( I \) if \( I_s \) were doubled?
3. How do we calculate the power dissipated in each branch?
4. What if we added another resistor in parallel to this configuration; how would it affect \( I \)?
5. How does changing the resistance in the left branch affect the overall equivalent resistance?

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### Tip
For parallel circuits, remember that the voltage across parallel branches remains the same, which simplifies the analysis of current distribution.

For the circuit below, Is = 10 A. Calculate the labelled current I, and give your answer in amps [A].

Learn how to calculate the labeled current I in a circuit with a 10 A current source, including detailed steps using parallel resistance and Ohm's law. Suitable for college or advanced high school physics students.

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