Question

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?

Answer 1

`50` Watt

Step-by-step explanation:

`P_(1)` = Initial signal power = 2 Watts

`r_(1)` = Initial range of distance to which signal is received = 3 miles

`P_(2)` = Final signal power = ?

`r_(2)` = Final range of distance to which signal is received = 15 miles

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

`\frac{P_(1)}{{r_(1)}^(2)} = \frac{P_(2)}{{r_(2)}^(2)}`

`\frac{2}{{3}^(2)} = \frac{P_(2)}{{15}^(2)}`

`(2)/(9) = (P_(2))/(225)`

`P_(2) = (2* 225)/(9)`

`P_(2) = 50` Watt