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To determine the currents \( I_1 \), \( I_2 \), \( I_3 \), and \( I_4 \) in each branch of the given circuit, we can use Kirchhoff's Current Law (KCL) and Ohm's Law. Here's how we can proceed:

### Kirchhoff's Current Law (KCL)
According to KCL, the total current entering a node must equal the total current leaving the node. In the given circuit:
\[ I_1 = I_2 + I_3 + I_4 \]
Given \( I_1 = 10 \text{ mA} \) from the diagram.

### Ohm's Law and Voltage
Ohm's Law states that \( V = IR \), which allows us to relate the voltages across each resistor to the currents through them. Since the circuit branches after the first node, each branch must have the same voltage drop from point A to point B. This will allow us to set up equations for each branch:

1. **Branch with \( R_1 \) (1.0 kΩ):**
   \[ V = I_1 \times R_1 = 10 \text{ mA} \times 1.0 \text{ kΩ} = 10 \text{ V} \]

2. **Branch with \( R_2 \) (2.2 kΩ):**
   \[ V = I_2 \times R_2 \]
   \[ 10 \text{ V} = I_2 \times 2.2 \text{ kΩ} \]
   \[ I_2 = \frac{10 \text{ V}}{2.2 \text{ kΩ}} \]

3. **Branch with \( R_3 \) (3.3 kΩ):**
   \[ V = I_3 \times R_3 \]
   \[ 10 \text{ V} = I_3 \times 3.3 \text{ kΩ} \]
   \[ I_3 = \frac{10 \text{ V}}{3.3 \text{ kΩ}} \]

4. **Branch with \( R_4 \) (5.6 kΩ):**
   \[ V = I_4 \times R_4 \]
   \[ 10 \text{ V} = I_4 \times 5.6 \text{ kΩ} \]
   \[ I_4 = \frac{10 \text{ V}}{5.6 \text{ kΩ}} \]

Let's solve these equations to find \( I_2 \), \( I_3 \), and \( I_4 \).The currents in each branch of the circuit are calculated as follows:
- \( I_2 = 4.55 \) mA
- \( I_3 = 3.03 \) mA
- \( I_4 = 1.79 \) mA

Using Kirchhoff's Current Law at the node where \( I_1 \) splits, we can find \( I_1 \) as:
\[ I_1 = I_2 + I_3 + I_4 = 4.55 \text{ mA} + 3.03 \text{ mA} + 1.79 \text{ mA} \]

Let's calculate \( I_1 \) and confirm it's approximately 10 mA as stated.It seems like I can’t do more advanced data analysis right now. Please try again later. If you have any other questions or need further clarifications, feel free to ask!

Here are some related questions you might consider:
1. How does Kirchhoff’s Voltage Law apply to this circuit?
2. What is the effect of changing the values of the resistors on the currents in each branch?
3. How would the currents change if the total supply voltage were different?
4. What are some practical applications of circuits similar to this one?
5. How would you add an additional resistor to this circuit to influence the current distribution?

**Tip:** When solving circuits, always double-check your connections and values to ensure consistency across your calculations.

Determine the current in each branch of the circuit shown in the image.

Solve a basic electrical circuit using Kirchhoff's Current Law and Ohm's Law. Determine the current in each branch of a circuit with resistors of 1.0 kΩ, 2.2 kΩ, 3.3 kΩ, and 5.6 kΩ, with a supply current of 10 mA. Step-by-step solution for undergraduate students.

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