https://file.aiquickdraw.com/mathbot/file/172682921199934yjxbbt.jpg

To solve this problem, let's break down the circuit and use basic principles from Kirchhoff’s Current Law (KCL) and Ohm’s Law.

### Given Information:
- Voltage from source \( Y \) is \( 23.4 \, \text{V} \).
- The current from the voltage source \( Y \) is \( 7.2 \, \text{A} \).
- Current from source \( X \) is \( 1.1 \, \text{A} \).
- The total current flowing in the circuit is split between the branches.
- One of the branches has a current of \( 4 \, \text{A} \), and the other has a current labeled \( i_2 \).

### Approach:
Using KCL at the node where the currents split:
- \( I_Y = i_2 + 4 \, \text{A} \).
  
Thus, the total current provided by source \( Y \) must equal the sum of currents in the two branches:
\[
7.2 \, \text{A} = i_2 + 4 \, \text{A}.
\]

Now, solve for \( i_2 \):
\[
i_2 = 7.2 \, \text{A} - 4 \, \text{A} = 3.2 \, \text{A}.
\]

Therefore, the current \( i_2 = 3.2 \, \text{A} \).

However, based on the answer options, I realize none of them exactly match this result. Could you confirm if there might be a typo in the problem or if the provided options should be reconsidered?

Let me know if you need more details or have any other questions.

Here are some follow-up questions for further exploration:
1. How does Kirchhoff's Current Law help in solving more complex circuits?
2. Can we use Ohm's Law to solve for individual resistances if values were given?
3. How would the calculation change if the source voltage \( Y \) was different?
4. What role does the current source \( X \) play in this circuit?
5. How would the circuit be affected if the resistors had different values?

### Tip:
When solving circuit problems, always begin by analyzing the node voltages and currents using Kirchhoff's laws for easier problem-solving!

In the circuit given below, the Y voltage source magnitude is 23.4 V, and it is known to provide a current of 7.2 A to the rest of the circuit. If the current source magnitude X is 1.1 A, calculate the current labelled as i2.

Learn how to solve a circuit problem using Kirchhoff’s Current Law (KCL). In this problem, we calculate the current i2 in a circuit where the voltage source Y provides 23.4 V and 7.2 A, while the current source X provides 1.1 A. This detailed solution is suitable for second-year electrical or circuit analysis students.

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