helpin a 120-volt circuit having a resistance of 12 ohms, the power W in watts when a current I is flowing through is given by W=120 I - 12 I^2. what is the maximum power, in watts, that can be...

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in a 120-volt circuit having a resistance of 12 ohms, the power W in watts when a current I is flowing through is given by W=120 I - 12 I^2. what is the maximum power, in watts, that can be delivered in this circuit?

Asked on by hollister7

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

w = 120 I - 12 i^2

To find the maximum value, we will need to find the derivativ'es zero.

==> w' = 120 - 24 I = 0

==> I = 120/24 = 5

Since the factor of I^2 is negative, then the function has Maximum value when I = 5

==> w = 120*I - 12 I^2

             = 120*5 - 12*5^2

             = 600 - 300 = 300

Then the maximum power is  W = 300 watts.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The equation power w is given by :

W = 120i - 12i^2

To find  the maximum power W.

To maximise W:

W/12 = (120i-12i^2)/12 = 10i-i^2

W/12 = 2*5i-i^2

W/12 =5^5  -5^2+2*5i-i^2

W/12 = 5^2 - (5 - i)^2

W/12  <5^2 , as  (5-i)^2 being a perfect square is always positive.

So the W/12 is maximum and equal to 5^2=25  when i = 5 amp.

Or the maximum power that could drawn is  W = 25*12 = 300 watts, when i = 5amp.

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