Problem 4 Two ideal voltage sources, \(E_{... [FREE SOLUTION] (2024)

Open in App

Open in App Log out

Chapter 1: Problem 4

Two ideal voltage sources, $E_{1}=100 \angle 0^{\circ} \mathrm{V}$ and$E_{2}=100 \angle 30^{\circ}$, are connected through an impedance $Z=j 5\Omega$. For both voltage sources the generator convention is used, whichmeans that the power delivered by the voltage sources is positive. a. Calculate the currents $I_{1}$ and $I_{2}$ delivered by both sources. b. Calculate the active power and the reactive power consumed by both sources. c. Which of the two sources is the generator? d. Calculate the losses.

Short Answer

Expert verified

The currents delivered by the sources are $I_{1} = 20 \angle -90^{\circ} A$, $I_{2} = 20 \angle -60^{\circ} A$. The complex powers consumed are $S_{1} = 0 + j2000 W$ and $S_{2} = 1732 - j1000 W$. Therefore, the generator is the 1st source and the losses in the system are 1732 W.

Step by step solution

Calculate Currents

To calculate the currents delivered by both sources, use Ohm's Law which states V=IZ, where V is the voltage, I is the current and Z is the impedance. Therefore, $I = V/Z$. For $I_{1}$, $I_{1} = E_{1} / Z = 100 \angle 0^{\circ} V / j5 \Omega = 20 \angle -90^{\circ} A$. And for $I_{2}$, $I_{2} = E_{2} / Z = 100 \angle 30^{\circ} V / j5 \Omega = 20 \angle -60^{\circ} A$

Calculate Power Consumed

The complex power consumed by the source can be calculated by $S = EI^*$, where $^*$ stands for conjugate. For source 1, $S_{1} = E_{1}I_{1}^* = 100 \angle 0^{\circ} V × 20 \angle 90^{\circ} A = 2000 \angle 90^{\circ} VA = 0 + j2000 W$. In a similar way, for source 2, $S_{2} = E_{2}I_{2}^* = 100 \angle 30^{\circ} V × 20 \angle 60^{\circ} A = 2000 \angle -30^{\circ} VA = 1732 - j1000 W$

Identify the Generator

A source that consumes reactive power is defined as a generator. Since the imaginary part of $S_{1}$ is positive and the imaginary part of $S_{2}$ is negative, the generator is source 1 which is delivering reactive power to the system

Calculate the Losses

The losses in the system can be calculated by subtracting the real power supplied by the generator from the total real power consumed by the two sources. So, $Losses = (S_{1} + S_{2}) - S_{generator} = (0 + j2000 W) + (1732 - j1000 W) - (0 + j2000 W) = 1732 W$

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

$Problem 4 Two ideal voltage sources, \(E_{... [FREE SOLUTION] (3)$

Most popular questions from this chapter

In a balanced three-phase system, the voltage between phases $a$ and $b$ is$V_{a b}=173.2 \angle 0^{\circ} \mathrm{V}$. The Y-connected load is $Z=10\angle 0^{\circ} \Omega$. The phase sequence is $a b c$. a. Calculate all phase-to-neutral voltages. b. Calculate all phase currents.In a balanced three-phase system, with a phase sequence $a b c$, theY-connected impedances are $Z=10 \angle 30^{\circ} \Omega$. If $V_{b c}=400\angle 90^{\circ} \mathrm{V}$, calculate a. $V_{c n}$ b. $I_{c n}$ c. $S$ consumed by the impedances .In a base system $\left|S_{b, 1}\right|$ and $\left|V_{b, 1}\right|$, the baseimpedance equals $\left|Z_{b, 1}\right| \cdot\left|Z_{b, 2}\right|$ is thebase impedance in a base system using $\left|S_{b, 2}\right|$ and $\left|V_{b,2}\right|$. Show that the following equation holds: $$ \left|Z_{b, 2}\right|=\left|Z_{b, 1}\right| \frac{\left|S_{b,1}\right|}{\left|S_{b, 2}\right|} \frac{\left|V_{b, 2}\right|^{2}}{\left|V_{b,1}\right|^{2}} $$A three-phase transmission line can be represented by a phase impedance of$Z=5+j 60 \Omega$ /phase. The complex power, measured at the sending end ofthe line, is $S_{1}=210+j 30 \mathrm{MVA}$. The line has a fixed line-to-linevoltage of $220 \mathrm{kV}$ at the sending end. a. Calculate the voltage and the complex power at the receiving end of theline. b. What are the transmission losses?In a three-phase circuit, the voltages of the phases $a$ and $b$, with respectto the neutral $n$, are $V_{a n}=140 \angle 45^{\circ} \mathrm{V}$ and $V_{bn}=90 \angle-15^{\circ} \mathrm{V}$. Calculate $V_{b a}$.

See all solutions

Recommended explanations on Physics Textbooks

Astrophysics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Physics of Motion

Read Explanation

Circular Motion and Gravitation

Read Explanation

Oscillations

Read Explanation

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free

This website uses cookies to improve your experience. We'll assume you're ok with this, but you can opt-out if you wish. Accept

Privacy & Cookies Policy

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.

Necessary

Always Enabled

Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.

Non-necessary

Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.

SAVE & ACCEPT

Problem 4 Two ideal voltage sources, \(E_{... [FREE SOLUTION] (2024)

Short Answer

Step by step solution

Calculate Currents

Calculate Power Consumed

Identify the Generator

Calculate the Losses

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Astrophysics

Geometrical and Physical Optics

Conservation of Energy and Momentum

Physics of Motion

Circular Motion and Gravitation

Oscillations

Study anywhere. Anytime. Across all devices.

Privacy Overview

References