### Electrical Engineering Problem: Circuit Analysis#### Problem Statement:3. Determine the currents \( I_1 \), \( I_2 \), and \( I_3 \). Then construct a phasor diagram to show that \( I_1 + I_2 + I_3 = 8 \angle (-30^\circ) \).#### Given Circuit Description:- The circuit consists of a parallel configuration.- There is a current source supplying \( 8 \angle 30^\circ \) amperes.- Three branches are connected to the source: - The first branch contains a resistor with a resistance of \( 5 \Omega \). - The second branch contains a resistor with a resistance of \( 2 \Omega \) in series with an inductor modeled by an impedance \( j10 \Omega \). - The third branch contains a resistor with a resistance of \( 6 \Omega \) in parallel with a capacitor modeled by an impedance \( -j2 \Omega \).#### Graphical Representation:The diagram shows the following components and their connections:- To the far left is the current source labeled \( 8 \angle 30^\circ \) A with an arrow indicating the direction of current flow.- In parallel: - The first branch is marked by a resistor \( R = 5 \Omega \) with current through it labeled \( I_1 \). - The second branch has a series connection of a resistor \( 2 \Omega \) and an inductor \( j10 \Omega \) with current through it labeled \( I_2 \). - The third branch has a resistor \( 6 \Omega \) in parallel with a capacitor \( -j2 \Omega \) with current through it labeled \( I_3 \).#### Analysis Required:1. Perform calculations to find the values of \( I_1 \), \( I_2 \), and \( I_3 \) using complex impedance analysis.2. Verify that the sum of the phasor currents \( I_1 \), \( I_2 \), and \( I_3 \) is equal to the source current \( 8 \angle -30^\circ \) A.3. Construct a phasor diagram to visually demonstrate the relationship.#### Steps to Solve:1. Calculate the impedance of each parallel branch.2. Use Ohm's Law (\( V = IZ \)) to find the voltage

Fig: Given circuit Calculate I1 , I 2 and I 3 using current division rule…

Answered: 3. Determine the currents I, I2, and…

3. Determine the currents I, I2, and I3. Then construct a phasor diagram to show that I + l2+ Iz = 84(-30°). 8L38 A jran

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.61P

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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

### Electrical Engineering Problem: Circuit Analysis

#### Problem Statement:
3. Determine the currents \( I_1 \), \( I_2 \), and \( I_3 \). Then construct a phasor diagram to show that \( I_1 + I_2 + I_3 = 8 \angle (-30^\circ) \).

#### Given Circuit Description:
- The circuit consists of a parallel configuration.
- There is a current source supplying \( 8 \angle 30^\circ \) amperes.
- Three branches are connected to the source:
- The first branch contains a resistor with a resistance of \( 5 \Omega \).
- The second branch contains a resistor with a resistance of \( 2 \Omega \) in series with an inductor modeled by an impedance \( j10 \Omega \).
- The third branch contains a resistor with a resistance of \( 6 \Omega \) in parallel with a capacitor modeled by an impedance \( -j2 \Omega \).

#### Graphical Representation:
The diagram shows the following components and their connections:
- To the far left is the current source labeled \( 8 \angle 30^\circ \) A with an arrow indicating the direction of current flow.
- In parallel:
- The first branch is marked by a resistor \( R = 5 \Omega \) with current through it labeled \( I_1 \).
- The second branch has a series connection of a resistor \( 2 \Omega \) and an inductor \( j10 \Omega \) with current through it labeled \( I_2 \).
- The third branch has a resistor \( 6 \Omega \) in parallel with a capacitor \( -j2 \Omega \) with current through it labeled \( I_3 \).

#### Analysis Required:
1. Perform calculations to find the values of \( I_1 \), \( I_2 \), and \( I_3 \) using complex impedance analysis.
2. Verify that the sum of the phasor currents \( I_1 \), \( I_2 \), and \( I_3 \) is equal to the source current \( 8 \angle -30^\circ \) A.
3. Construct a phasor diagram to visually demonstrate the relationship.

#### Steps to Solve:
1. Calculate the impedance of each parallel branch.
2. Use Ohm's Law (\( V = IZ \)) to find the voltage

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