Write the system of equations for the network using nodal analysis.Calculate the nodal voltagesFind Ir1,Ir2, and p12 This is a circuit diagram featuring multiple components, including resistors, voltage sources, and current sources. The circuit is depicted as follows:1. **Current Sources**: - A 5 A current source is located at the bottom left of the circuit. - An 8 A current source is located at the top center.2. **Voltage Sources**: - \( V_1 \) is a 20 V voltage source situated at the top right, directed towards the left. - \( V_2 \) is a 15 V voltage source at the center bottom, directed vertically upwards.3. **Resistors**: - \( R_1 \) is a 20 Ω resistor connected in series with the leftmost voltage source \( V_1 \). - \( R_2 \) is a 10 Ω resistor connected vertically between the 20 V source and the 15 V source. - \( R_3 \) is a 15 Ω resistor located at the top right. - \( R_4 \) is a 5 Ω resistor at the bottom right, connected in series with \( R_3 \).4. **Voltages across Resistors**: - \( v_1 \) is the voltage across \( R_1 \). - \( v_2 \) is the voltage across the first 20 V source. - \( v_3 \) is the voltage across the 10 Ω resistor \( R_2 \). - \( v_4 \) is the voltage across the 15 Ω resistor \( R_3 \).This diagram can be used to analyze circuit behavior, calculate voltages at various points, and determine current flow through the components. This setup demonstrates series and parallel configurations important for understanding circuit design and analysis.

Draw the Circuit: First apply KCL at Node V1: To find Ir1 apply KCL at node V1:5+Ir1=8Ir1=3 A Apply…

Answered: Write the system of equations for the…

Engineering

Electrical Engineering

Write the system of equations for the network using nodal analysis. Calculate the nodal voltages Find Ir1,Ir2, and p12

Delmar's Standard Textbook Of Electricity

7th Edition

ISBN:9781337900348

Author:Stephen L. Herman

Publisher:Stephen L. Herman

Chapter7: Parallel Circuits

Section: Chapter Questions

Problem 3PP: Using the rules for parallel circuits and Ohmslaw, solve for the missing values....

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Concept explainers

Nodal Analysis

In the analysis of any electric circuit, nodal analysis is the method of determining the potential difference or voltage between different nodes in an electric circuit. A node is a point where two or more branches connect each other. In the nodal analysis, the voltages are determined in the terms of branch currents. The nodal analysis is also known as the node voltage method or branch current method. The nodal analysis method is one of the several applications of Kirchhoff's Current Law (KCL).

Question

Write the system of equations for the network using nodal analysis.

Calculate the nodal voltages

Find Ir1,Ir2, and p12

This is a circuit diagram featuring multiple components, including resistors, voltage sources, and current sources. The circuit is depicted as follows:

1. **Current Sources**:
- A 5 A current source is located at the bottom left of the circuit.
- An 8 A current source is located at the top center.

2. **Voltage Sources**:
- \( V_1 \) is a 20 V voltage source situated at the top right, directed towards the left.
- \( V_2 \) is a 15 V voltage source at the center bottom, directed vertically upwards.

3. **Resistors**:
- \( R_1 \) is a 20 Ω resistor connected in series with the leftmost voltage source \( V_1 \).
- \( R_2 \) is a 10 Ω resistor connected vertically between the 20 V source and the 15 V source.
- \( R_3 \) is a 15 Ω resistor located at the top right.
- \( R_4 \) is a 5 Ω resistor at the bottom right, connected in series with \( R_3 \).

4. **Voltages across Resistors**:
- \( v_1 \) is the voltage across \( R_1 \).
- \( v_2 \) is the voltage across the first 20 V source.
- \( v_3 \) is the voltage across the 10 Ω resistor \( R_2 \).
- \( v_4 \) is the voltage across the 15 Ω resistor \( R_3 \).

This diagram can be used to analyze circuit behavior, calculate voltages at various points, and determine current flow through the components. This setup demonstrates series and parallel configurations important for understanding circuit design and analysis.

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