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=120I-12I². What is the maximum power, in watts, that can be delivered in this circuit?

maximum power = 300 W

Explanation:

Ohm's law: Ohm's law state that the current flowing through a metallic conductor, is directly proportional to the potential difference applied across its end. mathematically it is expressed as,

V = IR ... Equation 1

Where V = potential difference, I = current, R = Resistance of the conductor.

If the power flowing through is gives as

W = 120I - 12I² ... Equation 2

To get the maximum power we differentiate of equation 2 and equate to zero

dW/dt = 0

120 - 24l = 0 ... equation 3

Making I the subject of the equation,

I = 120/24 = 5 A.

Suubstituting the value of I into Equation 2

W = 120 (5) - 12 (5) ²

W = 600 - 300

W = 300 W.

Therefore maximum power = 300 W