Question

the power generated by an electrical circuit (in watts) as a function of its current C (in amperes) is modeled by P(c)= -15c(c-8) What current will produce the maximum power?

Answer 1

The maximum power is produced at current = 4 A

Explanation:

Given:

The power generated by an electrical circuit (in watts) is modeled as a function of current as:

`P(c)=-15c(c-8)`

To find the current that will produce the maximum power.

Solution:

The function can be simplified using distribution.

`P(c)=-15c^2+120c`

We know that the power will be maximum at the point where the slope of the equation will be = 0 i.e. parallel to x-axis.

Finding the slope of the function using derivative.

`(dP)/(dc)=-30c+120`

We will equate the slope = 0 to get the current for maximum power.

Thus, we have:

`-30c+120=0`

Subtracting both sides by 120.

`-30c+120-120=0-120`

`-30c=-120`

Dividing both sides by -30.

`(-30c)/(-30)=(-120)/(-30)`

∴
`c=4`

Thus, the maximum power is produced at current = 4 A

Answer 2

c = 4 A

Explanation:

The given function P(c) = - 15 c (c-8) is actually quadratic function:

P(c) = - 15c² + 120c or parabola

The standard form of a quadratic function is:

y = ax² + bx + c

For which x is the maximum of the parabola we can find with this formula

x = - b/2a

in this case a = -15 and b = 120 and input variable is current c

c = - 120/(2 · (-15)) = - 120/ (-30) = 4 A

c = 4 A

God with you!!!