Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

a) What current is needed to transmit1.00ร—102MWof power at480V? (b) What power is dissipated by the transmission lines if they have a1.00ฮฉresistance? (c) What is unreasonable about this result? (d) Which assumptions are unreasonable, or which premises are inconsistent?

Short Answer

Expert verified
  1. Current needed to transmit the given power is2.08ร—105A.
  2. Power dissipated by the transmission line is43.3GW.
  3. Power dissipated in transmission is huge.
  4. The voltage is too low.

Step by step solution

01

Definition of power and relation between potential difference & power:

Power: The power of a process is the amount of some type of energy converted into a different type divided by the time intervalฮ”tin which the process occurred:

P=ฮ”Eฮ”t โ€ฆ.. (1)

The SI unit of power is the watt (W).

Because the potential difference across a resistor is given byฮ”V=IRit can be expressed into the power delivered to a resistor as

P=I2R

P=(ฮ”V)2R โ€ฆ.. (2)

The energy delivered to a resistor be electrical transmission appears in the form of internal energy in the resistor.

02

Given data and required data.

The power output of the transmission line is:

cPout=(1.00ร—102MW)(106W1MW)=1.00ร—108W

The voltage at which the power is transmitted,ฮ”V=480V.

The resistance of the transmission lines is:R=1.00ฮฉ.

In part (a), we are asked to determine the current needed to transmit a power Poutat voltage ฮ”V.

03

(a) Calculation of current using the power output of transmission line.

The power output of the transmission line is found from equation (1):

Pout=Iฮ”V

Solve the above equation for I:

I=Poutฮ”V

Substitute numerical values in the above expression.

I=1.00ร—108W480V=2.08ร—105A

Therefore, current needed to transmit the given power is 2.08ร—105A.

04

(b) Calculation of power dissipated.

The power dissipated within the transmission lines before reaching its destination is found from equation (2):

P=I2R

Entering values for I and R, and you obtain:

P=(2.08ร—105A)2(1.00ฮฉ)=4.34ร—1010W=(4.34ร—1010W)(1GW109W)=43.3GW

Hence, Power dissipated by the transmission line is 43.3GW.

05

 Step 5: (c) Unreasonable about result:

The power dissipated within the transmission lines is huge. It is even greater than the power output of the transmission lines.

06

(d) Define which assumptions are unreasonable, or which premises are inconsistent:

The voltage is too low. Such a transmission line in real life would have much higher voltage and low current so that the power dissipated in the line is reduced.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

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

Get started for free

Study anywhere. Anytime. Across all devices.

Sign-up for free