A. In a circuit with resistance 10 ohms, power 𝑃 (measured in watts) is equal to 10𝐼^2 , where 𝐼 is the current measured in amperes. When 𝐼=6 amperes, what is the rate of change of 𝑃 with respect to 𝐼 ?

Question

B. If we additionally know that when 𝐼=6 , the current is increasing at 0.2 amperes per minute, at what rate (with respect to time) is power increasing at that moment?

C. What units is your answer measured in?

Answer 1

P = 10I^2
dP/dt = 2I dI/dt
again, plug in your numbers
units? just look at the units in the fraction that is the derivative

Answer 2

Unfortunately this is my weakest topic in Calculus so far, I'm still not able to find the correct answer.

I used product rule to break up 10*I^2

Should I even be doing this? Please elaborate further if possible. (Something a 5th grader could comprehend haha)

Answer 3

read up on the chain rule
If P is a function of I, and I is a function of t, then
dP/dt = dP/dI * dI/dt