Electricity question on the power generated by power stations.

In summary, the power lost per kilometre heating the conductors is 7.65MW, with a resistance of 0.034Ω per kilometre and a current of 15kA.
  • #1
Delpo
4
0

Homework Statement



2)The power stations providing electricity for the National Grid generate electricity at 25kV. The typical demand on an average winter's day in the north-west of England is 6000MW. The current output form the generators is 240kV. Transformers raise the transmission voltage to 400kV. Assuming 100% efficiency in the transformers, the current is 15kA. Each pair of 400kV supergrid conductors has a resistance of 0.034Ωk/m.
How much power is lost per kilometre heating the conductors?
Books answer:7.65MW

Homework Equations



P=W/t=VQ/t=VI
V=IR
R=VI

The Attempt at a Solution


Can type my working out sorry.
 
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  • #2
Delpo said:

Homework Statement



2)The power stations providing electricity for the National Grid generate electricity at 25kV. The typical demand on an average winter's day in the north-west of England is 6000MW. The current output form the generators is 240kV. Transformers raise the transmission voltage to 400kV. Assuming 100% efficiency in the transformers, the current is 15kA. Each pair of 400kV supergrid conductors has a resistance of 0.034Ωk/m.
How much power is lost per kilometre heating the conductors?
Books answer:7.65MW

Homework Equations



P=W/t=VQ/t=VI
V=IR
R=VI

The Attempt at a Solution


Can type my working out sorry.

We don't know how to help if you don't show your attempt...
 
  • #3
We can't help you unless we can see you have tried to solve it.
 
  • #4
Are you sure you copied that text correctly? It seems to contain several errors. For example it should be 0.034Ω/km, not 0.034Ωk/m.
So each km of conductor has a resistance of 0.034Ω. The current is 15kA.
Now you just have to apply your equations.
V=IR
P=VI
 
  • #5


I would like to provide a clarification on the terminology used in this question. The power stations mentioned in the question are most likely referring to power plants, which are facilities that generate electricity. The National Grid is a network of power lines and transformers that distribute electricity from power plants to homes and businesses.

Now, to answer the question, we need to use the formula P=VI, where P is power in watts, V is voltage in volts, and I is current in amperes. We are given the voltage and current values, so we can calculate the power output of the generators as follows:

P = 240kV x 15kA = 3.6MW

This is the power output of the generators, but this is not the power that reaches the consumers. The power needs to be transmitted through the supergrid conductors, which have a resistance of 0.034Ωk/m. This means that for every kilometer of transmission, there will be a power loss due to the heating of the conductors. To calculate this power loss, we can use the formula P=I^2R, where P is power in watts, I is current in amperes, and R is resistance in ohms.

Since we are given the current and resistance values, we can calculate the power loss per kilometer as follows:

P = (15kA)^2 x 0.034Ωk/m = 7.65MW

Therefore, the power lost per kilometer is 7.65MW. It is important to note that this calculation assumes 100% efficiency in the transformers, which is not always the case in real-world scenarios. In reality, there will be some power loss due to inefficiencies in the transformers, which may result in a slightly different value for the power lost per kilometer.
 

1. How is electricity generated in power stations?

Electricity is generated in power stations through a process called electromagnetic induction. This involves spinning large turbines inside a generator, which creates a magnetic field that causes electrons to move and generate electricity.

2. What fuels are commonly used to generate electricity in power stations?

The most common fuels used in power stations are coal, natural gas, and nuclear energy. However, some power stations are also powered by renewable energy sources such as wind, solar, and hydro power.

3. How much electricity can a power station generate?

The amount of electricity a power station can generate depends on its size and the type of fuel used. On average, a large power station can generate enough electricity to power hundreds of thousands of homes.

4. How is the electricity from power stations distributed to homes and businesses?

Once generated, electricity from power stations travels through a network of power lines and transformers to reach homes and businesses. This network is called the electrical grid.

5. Are power stations harmful to the environment?

The generation of electricity in power stations can have negative impacts on the environment, such as air and water pollution. However, advancements in technology have allowed for cleaner and more sustainable methods of electricity generation to be used in power stations.

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