SOLUTION: Electricians can calculate the electrical current in amps A by using the formula A= √w/√r, where w is the power in watts and r the resistance in ohms.
How much elec
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Question 556740: Electricians can calculate the electrical current in amps A by using the formula A= √w/√r, where w is the power in watts and r the resistance in ohms.
How much electrical current is running through a microwave oven that has 850 watts of power and 5 ohms of resistance?
Write your answer in simplest radical form and then estimate the amount of current to the nearest tenth.
Hint: There are two answers for this problem - one a radical and one a decimal.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The equation you are given is:
.
.
in which A is the current in amperes, w is the power consumed in watts, and r is the resistance in ohms.
.
Next you are told that a microwave oven consumes 850 watts and the resistance of the oven is 5 ohms. Substitute these two values for w and r in the equation, and the equation becomes:
.
.
By the properties of square roots, the right side of this equation is equal to the overall square root of the two given values. In other words, the square root of 850 divided by the square root of 5 is equal to the square root of 850 divided by 5. In equation form this can be written as:
.
.
Divide 5 into 850 and you get 170. Therefore, the equation can be simplified to:
.
and don't forget that the units for current is amperes.
.
This may be the answer that you are to provide in the form of a radical.
.
Next you are supposed to estimate the current. In other words, estimate the square root of 170 to the nearest tenth of an ampere.
.
One way to do this is to recognize that 12 squared (12 times 12) is 144. Then 13 squared (13 times 13) is 169. And then 14 squared (14 times 14) is 196. From this you can tell that 13 times 13 is very, very close to 170. So as an estimate you might say that the current is in the vicinity of exactly 13.0 amperes. You could try multiplying by hand 13.1 times 13.1 and see what its value is. If you do that you get 171.16. This result is 1.16 bigger than 170. And you know already that 13.0 times 13.0 is 169, and this is 1.00 less than 170. Therefore, it is likely that 13.0 is closer to being the square root of 170 than 13.1 is.
.
In summary, the exact answer is:
.
amperes
.
and the estimated answer (to the nearest tenth) is 13.0 amperes.
.
I hope this helps you to understand this problem a little better.
.
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