Find out the value of the unknown currents

Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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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.
Transcribed Image Text: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 (V1) present in the circuit. 

The unknown currents are I1, I2 and I3.

The application of KCL at node V1 gives

12=V16+V14+V112+6=>V116+14+112=6=>V1612=6=>V1=12 V

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