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If a transmitter uses a signal power of 2 Watts that can be reliably received within a distance of up to 3miles, what is the lowest amount of signal power that would be required for a similar signal to be received within a distance of 15 miles?

Respuesta :

Answer:

[tex] 50[/tex] Watt

Explanation:

[tex]P_{1}[/tex] = Initial signal power = 2 Watts

[tex]r_{1}[/tex] = Initial range of distance to which signal is received = 3 miles

[tex]P_{2}[/tex] = Final signal power = ?

[tex]r_{2}[/tex] = Final range of distance to which signal is received = 15 miles

Intensity is inversely proportional to square of the distance from the source, hence

[tex]\frac{P_{1}}{{r_{1}}^{2}} = \frac{P_{2}}{{r_{2}}^{2}}[/tex]

[tex]\frac{2}{{3}^{2}} = \frac{P_{2}}{{15}^{2}}[/tex]

[tex]\frac{2}{9} = \frac{P_{2}}{225}[/tex]

[tex]P_{2} = \frac{2\times 225}{9}[/tex]

[tex]P_{2} = 50[/tex] Watt

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