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Llana [10]
4 years ago
9

A homeowner is installing a swimming pool. You have been asked to install a circuit to operate a 600-watt underwater light and a

circulating pump. The motor nameplate reveals that the pump has a current draw of 8.5 amperes. The devices are considered continuous duty. Can the power to operate both of these devices be supplied by a single 20-ampere circuit?
Mathematics
1 answer:
insens350 [35]4 years ago
3 0

Answer:

The answer is given below

Step-by-step explanation:

The loads in the circuit are continuous duty, so the circuit can only loaded to 80% of its current rating.

Calculate 80% current rating of the circuit breaker.

Icb = [ 80/100] (20 A)

     =  (O.8) (20 A )

     = 16 A

Now we assume that the value of supply voltage is 120 V

Now we will calculate current flows via under water light which will be taken as  Load 1

<em>Ii = </em>500 W/120 V

  = 4.167 A

Current via the circulating pump which will be taken as Load 2 IS 8.5 A

<em>I = </em>load1 + load 2

<em>    = 4.167 A + 8.5 A</em>

<em>   = 12.67 A</em>

The total current in the circuit obtained which is less than the circuit breaker rating current. Therefore, the power can be operated for both the loads.

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a) For this case we can use the fact that sin (\pi/3) = \frac{\sqrt{3}}{2}

And for this case since we ar einterested on -\frac{\pi}{3} and we know that the if we are below the y axis the sine would be negative then:

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Step-by-step explanation:

For this case we can use the notable angls given on the picture attached.

Part a

For this case we can use the fact that sin (\pi/3) = \frac{\sqrt{3}}{2}

And for this case since we ar einterested on -\frac{\pi}{3} and we know that the if we are below the y axis the sine would be negative then:

sin (-\pi/3) = -\frac{\sqrt{3}}{2}

Part b

From definition we can use the fact that tan x= \frac{sin x}{cos x} and we got this:

tan (5\pi/4) = \frac{sin(5\pi/4)}{cos(5\pi/4)}

We can use the notabl angle \pi/4 and we know that :

sin (\pi/4) = cos(\pi/4) = \frac{\sqrt{2}}{2}

Then we know that 5\pi/4 correspond to 225 degrees and that correspond to the III quadrant, and we know that the sine and cosine are negative on this quadrant. So then we have this:

tan (5\pi/4) = \frac{sin(5\pi/4)}{cos(5\pi/4)}= \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1

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