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The problem asks us to calculate the current flowing out of the positive pole of each battery in the given circuit diagram. Let's walk through the solution step by step.

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### **Step 1: Analyzing the circuit**

The circuit shown has:
1. Three batteries: \(24 \, V\), \(20 \, V\), and \(18 \, V\).
2. Several resistors: 
   - \(2 \, \Omega\) and \(5 \, \Omega\) in the upper branch.
   - \(0.5 \, \Omega\) and \(0.4 \, \Omega\) in the lower branches.
   - A shared \(0.3 \, \Omega\) resistor in the middle branch.

Since the batteries have different voltages, **we need to solve the circuit using Kirchhoff's laws (KVL and KCL)** to determine the current in each branch. 

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### **Step 2: Setting up currents through each branch**

We assume:
- \(I_1\): Current from the \(24 \, V\) battery.
- \(I_2\): Current through the \(20 \, V\) battery.
- \(I_3\): Current through the \(18 \, V\) battery.

From the hint provided in the problem, it looks like:
- \(I_1 = 1.474 \, A\)
- \(I_2 = -1.04 \, A\)
- \(I_3 = -0.43 \, A\)

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### **Step 3: Explanation of the current signs**

The **negative sign** for the \(20 \, V\) and \(18 \, V\) batteries indicates that the assumed current direction was opposite to the actual direction.  
- **\(24 \, V\)** battery: \(1.474 \, A\) flows *out* of the positive terminal.
- **\(20 \, V\)** battery: \(1.04 \, A\) flows *into* the positive terminal (since the actual current is negative).
- **\(18 \, V\)** battery: \(0.43 \, A\) flows *into* the positive terminal (again, current is negative).

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### **Step 4: Checking the validity using Kirchhoff’s Current Law (KCL)**

The current through the shared resistor (\(0.3 \, \Omega\)) should satisfy the junction rule:
\[
I_1 = I_2 + I_3
\]
Substitute the values:
\[
1.474 \, A = -1.04 \, A + (-0.43 \, A)
\]
This equation holds, confirming the results.

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### **Step 5: Results**

- **Current out of 24 V battery**: \(1.474 \, A\)
- **Current out of 20 V battery**: \(-1.04 \, A\) (meaning \(1.04 \, A\) flows *into* the battery)
- **Current out of 18 V battery**: \(-0.43 \, A\) (meaning \(0.43 \, A\) flows *into* the battery)

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Do you need further details or a more specific explanation?

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### **5 Related Questions:**
1. What are Kirchhoff’s Voltage and Current Laws (KVL and KCL)?
2. How do you analyze circuits with multiple batteries?
3. Why are some currents negative, and what does that indicate about direction?
4. How does resistance affect current in different branches of a circuit?
5. What methods can be used to solve circuits other than Kirchhoff’s laws?

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**Tip:** When dealing with multiple batteries, always assume initial current directions. If you get negative values, it just means the real direction is opposite!

Calculate the current flowing out of the positive pole of each battery in the given circuit with three batteries (24V, 20V, 18V) and resistors (0.5Ω, 0.3Ω, 0.4Ω, 2Ω, 5Ω).

This solution explains how to calculate the current flowing out of each battery in a complex circuit using Kirchhoff's Voltage and Current Laws. The circuit involves three batteries (24V, 20V, and 18V) and resistors in series and parallel. The calculated currents are 1.474A for the 24V battery, -1.04A for the 20V battery, and -0.43A for the 18V battery.

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