Imagine that the satellite described in the problem introduction is used to transmit television signals. You have a satellite TV
1 answer:
Complete Question
A satellite in geostationary orbit transmits data using electromagnetic radiation, positioned 35,000 km above the Earth's surface, with an isotropic power output of 1 kW (although actual satellite antennas transmit with less power but more directionally).
Now, imagine this satellite relays television signals and you have a satellite TV receiver with a circular dish of radius R that focuses the electromagnetic energy from the satellite onto a receiver with a surface area of 5 cm2.
What radius R must this dish have to achieve an electric field vector amplitude of 0.1 mV/m at the receiver?
Assuming your house is situated directly beneath the satellite (as calculated previously), that the dish reflects all incoming signals to the receiver without any losses in the reception process, and that the dish has a curvature where R refers to its projection perpendicular to the direction of the incoming signal.
Present your answer in centimeters, rounded to two significant figures.
Answer:
The radius of the dish is
Explanation:
The question indicates that
The orbital radius is =
The power output is
The electric vector amplitude is noted as
The receiver's area is
Overall, the intensity of the dish can be mathematically expressed as
Here, A represents the area of the orbit, described as the surface area of a sphere, thus calculated as
Ultimately, substituting the values into the intensity equation
Therefore, the intensity received by the dish can be mathematically evaluated as
With c symbolizing the speed of light which has a constant value of
is the permittivity of free space, valued at
indicates the electric field present on the dish
Assuming no loss, the intensity from the satellite equals the intensity hitting the receiver dish
Setting the electric field intensity as the subject of the formula
Inputting values
The power incident on the dish reflects what is delivered to the receiver
Where symbolizes the power incident on the dish expressed mathematically as
And is the incident power on the dish represented as
Equating the two gives
Solving for R yields
Substituting values gives
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Answer:
The total energy saving achieved will be 0.8 KWH
Explanation:
It is provided that there are 50 long light bulbs rated at 100 W, thus the total power consumed by 50 bulbs equals 100×50 = 5000 W = 5 KW
Additionally, 30 bulbs are rated at 60 W
Consequently, the total power consumption of 30 bulbs is 30×60 = 1800 W = 1.8 KW
The cumulative power of all 80 bulbs is 1.8 + 5 = 6.8 KW
Considering the operation time of 3 hours
We know that energy
Now, the power consumption per CFL bulb equals 25 W
Thus for 80 bulbs, power equals 80×25 = 2000 W = 2 KW
So the energy for 80 bulbs amounts to 2×3 = 6 KWH
Hence, the overall energy saving is 6.8 - 6 = 0.8 KWH