
A thermal power plant produces electric power of at , which is to be transported to a place away from the power plant for consumers' usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformers, the dissipation is much smaller. In this method, a step-up transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers' end, a step-down transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with power factor unity. All the currents and voltages mentioned are rms values.
If the direct transmission method with a cable of resistance is used, the power dissipation (in %) during transmission is?
Answer
480k+ views
Hint: The power dissipated in a transmission line is proportional to square of the current. Here to find the power, we are given the values of electrical power produced and the voltage. Using the resistance per kilometer, we can find total resistance across cable. By substituting these values in the formula for power dissipated, we can find the percentage loss in power.
Formula used:
Complete answer:
Here,
Resistance,
Then, total resistance across cable
We have,
---------- 1
Where,
is the power dissipated
is the rms current
is the resistance
We have,
Current,
Where,
is the electrical power
is the voltage
Given that, and . Then
Current,
Substitute the value of and in equation 1, we get,
So, the correct answer is “Option B”.
Note:
The transmission over long distances creates power losses. The major part of the energy losses comes from power lines and Joule effect in transformers. The energy is lost as heat in the conductors. And the transmission lines have some amount of resistance. Hence power loss in transmission lines cannot be avoided.
Formula used:
Complete answer:
Here,
Resistance,
Then, total resistance across
We have,
Where,
We have,
Current,
Where,
Given that,
Current,
Substitute the value of
So, the correct answer is “Option B”.
Note:
The transmission over long distances creates power losses. The major part of the energy losses comes from power lines and Joule effect in transformers. The energy is lost as heat in the conductors. And the transmission lines have some amount of resistance. Hence power loss in transmission lines cannot be avoided.
Recently Updated Pages
Master Class 9 General Knowledge: Engaging Questions & Answers for Success

Master Class 9 English: Engaging Questions & Answers for Success

Master Class 9 Science: Engaging Questions & Answers for Success

Master Class 9 Social Science: Engaging Questions & Answers for Success

Master Class 9 Maths: Engaging Questions & Answers for Success

Class 9 Question and Answer - Your Ultimate Solutions Guide

Trending doubts
Give 10 examples of unisexual and bisexual flowers

Draw a labelled sketch of the human eye class 12 physics CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Differentiate between insitu conservation and exsitu class 12 biology CBSE

What are the major means of transport Explain each class 12 social science CBSE

Draw a diagram of a flower and name the parts class 12 biology ICSE
