Question

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−10I2. What current supplies the maximum wattage? 36

360

12

6

Answer 1

The current supplies the maximum wattage is 6 Ampere.

Explanation:

Given : In a 120-volt circuit having a resistance of 10 ohms, the power W in watts when a current I is flowing through is given by
`W=120I-10I^2`

To find : What current supplies the maximum wattage?

Solution :

The equation of power is

`W=120I-10I^2`

Derivate w.r.t x,

`W'=120-20I`

For critical point put it to zero,

`120-20I=0`

`20I=120`

`I=(120)/(20)`

`I=6`

Now, again derivate w.r.t I,

`W''=-24<0`

It is maximum at I=6 A

Therefore, the current supplies the maximum wattage is 6 Ampere.