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An antenna in air radiates a total power of 100KW so that a maximum radiated electric field strength of 12 m V/m is measured 20 km from the antenna. What would be its maximum power gain if hr = 98%
- a)9.408 × 10–3
- b)9.2 × 10–2
- c)up>(c) 0.932
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
An antenna in air radiates a total power of 100KW so that a maximum r...
To calculate the maximum power gain of the antenna, we need to use the formula:
Power Gain (G) = (E^2 * r^2) / (P * 4π * R^2)
Where:
E is the maximum electric field strength (12 mV/m)
r is the distance from the antenna where the measurement is taken (20 km = 20,000 m)
P is the total power radiated by the antenna (100 kW = 100,000 W)
R is the distance from the antenna to the point where we want to calculate the power gain
Let's calculate the power gain using the given values:
Power Gain (G) = (E^2 * r^2) / (P * 4π * R^2)
= (12 mV/m)^2 * (20,000 m)^2 / (100,000 W * 4π * R^2)
= (0.012 V/m)^2 * (20,000 m)^2 / (100,000 W * 4 * 3.1416 * R^2)
= (0.000144 V^2/m^2) * (400,000,000 m^2) / (125,664 W * R^2)
= 57.6 V^2 / (125,664 W * R^2)
Now, we know that the efficiency (hr) of the antenna is given as 98%, which means that the power radiated by the antenna is 98% of the total power input.
P = 0.98 * 100 kW = 98,000 W
Substituting this value into the power gain formula:
Power Gain (G) = 57.6 V^2 / (125,664 W * R^2)
= 57.6 / (125,664 * R^2) * V^2/W
Since the power gain is a dimensionless quantity, we can remove the units V^2/W from the equation:
Power Gain (G) = 57.6 / (125,664 * R^2)
Now, let's substitute the given value of R (20 km = 20,000 m) into the equation:
Power Gain (G) = 57.6 / (125,664 * (20,000 m)^2)
= 57.6 / (125,664 * 400,000,000 m^2)
≈ 9.408 × 10^(-3)
Therefore, the maximum power gain of the antenna is approximately 9.408 × 10^(-3), which corresponds to option A.
Power Gain (G) = (E^2 * r^2) / (P * 4π * R^2)
Where:
E is the maximum electric field strength (12 mV/m)
r is the distance from the antenna where the measurement is taken (20 km = 20,000 m)
P is the total power radiated by the antenna (100 kW = 100,000 W)
R is the distance from the antenna to the point where we want to calculate the power gain
Let's calculate the power gain using the given values:
Power Gain (G) = (E^2 * r^2) / (P * 4π * R^2)
= (12 mV/m)^2 * (20,000 m)^2 / (100,000 W * 4π * R^2)
= (0.012 V/m)^2 * (20,000 m)^2 / (100,000 W * 4 * 3.1416 * R^2)
= (0.000144 V^2/m^2) * (400,000,000 m^2) / (125,664 W * R^2)
= 57.6 V^2 / (125,664 W * R^2)
Now, we know that the efficiency (hr) of the antenna is given as 98%, which means that the power radiated by the antenna is 98% of the total power input.
P = 0.98 * 100 kW = 98,000 W
Substituting this value into the power gain formula:
Power Gain (G) = 57.6 V^2 / (125,664 W * R^2)
= 57.6 / (125,664 * R^2) * V^2/W
Since the power gain is a dimensionless quantity, we can remove the units V^2/W from the equation:
Power Gain (G) = 57.6 / (125,664 * R^2)
Now, let's substitute the given value of R (20 km = 20,000 m) into the equation:
Power Gain (G) = 57.6 / (125,664 * (20,000 m)^2)
= 57.6 / (125,664 * 400,000,000 m^2)
≈ 9.408 × 10^(-3)
Therefore, the maximum power gain of the antenna is approximately 9.408 × 10^(-3), which corresponds to option A.
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Community Answer
An antenna in air radiates a total power of 100KW so that a maximum r...
= 0.0096
Maximum power gain!
G = ηr Gd
= 0.98 × 0.0096
= 9.408 × 10–3
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An antenna in air radiates a total power of 100KW so that a maximum radiated electric field strength of 12 m V/m is measured 20 km from the antenna. What would be its maximum power gain if hr = 98%a)9.408 × 10–3b)9.2 × 10–2c)up>(c) 0.932d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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