Find out the value of the unknown currents. The image illustrates an electrical circuit featuring a combination of current sources and resistors. ### Components and Configuration:1. **Current Sources:** - On the left side, there is a 12 A current source entering the circuit. - On the right side, there is a 6 A current source exiting the circuit.2. **Resistors:** - **R1** is a 6 Ω resistor. The current through R1 is labeled as I1. - **R2** is a 4 Ω resistor. The current through R2 is labeled as I2. - **R3** is a 12 Ω resistor. The current through R3 is labeled as I3.3. **Nodes:** - **Node 1** is marked at the top junction of the resistors, connecting them across the circuit. - The **Ground node** is indicated at the bottom, providing a reference point for measuring voltage in the circuit.4. **Voltage:** - Voltage across the nodes is marked as V1.### Diagram Explanation:- The circuit is a part of a larger network, and it shows how current sources and resistors are interconnected.- The resistors R1, R2, and R3 are in parallel configuration across Node 1 and the ground.- The configuration is useful for analyzing electric networks, with applications in determining current distribution and voltage levels using techniques like Node Voltage Analysis.

Answered: Find out the value of the unknown…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Find out the value of the unknown currents.

The image illustrates an electrical circuit featuring a combination of current sources and resistors.

### Components and Configuration:

1. **Current Sources:**
- On the left side, there is a 12 A current source entering the circuit.
- On the right side, there is a 6 A current source exiting the circuit.

2. **Resistors:**
- **R1** is a 6 Ω resistor. The current through R1 is labeled as I1.
- **R2** is a 4 Ω resistor. The current through R2 is labeled as I2.
- **R3** is a 12 Ω resistor. The current through R3 is labeled as I3.

3. **Nodes:**
- **Node 1** is marked at the top junction of the resistors, connecting them across the circuit.
- The **Ground node** is indicated at the bottom, providing a reference point for measuring voltage in the circuit.

4. **Voltage:**
- Voltage across the nodes is marked as V1.

### Diagram Explanation:

- The circuit is a part of a larger network, and it shows how current sources and resistors are interconnected.
- The resistors R1, R2, and R3 are in parallel configuration across Node 1 and the ground.
- The configuration is useful for analyzing electric networks, with applications in determining current distribution and voltage levels using techniques like Node Voltage Analysis.

Expert Solution

Step 1

According to Kirchhoff's current law (KCL), the sum of all the currents entering a node will be equal to the sum of all the currents leaving that node.

In this case, there is only one node ( $V_{1}$ ) present in the circuit.

The unknown currents are $I_{1}, I_{2} and I_{3}$ .

The application of KCL at node $V_{1}$ gives

$12 = \frac{V_{1}}{6} + \frac{V_{1}}{4} + \frac{V_{1}}{12} + 6 = > V_{1} (\frac{1}{6} + \frac{1}{4} + \frac{1}{12}) = 6 = > V_{1} (\frac{6}{12}) = 6 = > V_{1} = 12 V$

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