the equation w=120I-12I^2 represents the power(W) in watts, of a 120 volt circuit having a resistance of 12 ohms. when a current (I) is flowing through the circuit what is the max. power in watts that can delivered in this circuit
2007-10-28 05:22:16 · 3 answers · asked by ~USA~ 2 in Science & Mathematics ➔ Mathematics
you get the maximum by equalizing the derivative to zero
dw/dI = 120 - 24I = 0
I = 120/24 = 5 amp is where the max occurs
so max w = 120*5 - 12*5^2
w = 300 Watts
2007-10-28 05:26:42 · answer #1 · answered by landonastar 3 · 0⤊ 0⤋
dW / dI = 120 - 24I
To find critical value, equate to 0
120 - 24I = 0
I = 120/24 = 5
now at I = 5 the power will be maximum
so W = 120(5) - 12(5)^2
= 600 - 300
= 300 Watts.
2007-10-28 05:32:38 · answer #2 · answered by gauravragtah 4 · 0⤊ 0⤋
w=120I-12I^2
Max occurs when I = -b/2a = -120/-24= 5
So w max = 120(5) - 12(5^2) = 600-300 = 300 watts
2007-10-28 05:29:35 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋