In a circuit with resistance 10 ohms, power 𝑃 (measured in watts) is equal to 10𝐼2 , 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

In a circuit with resistance 10 ohms, power  𝑃  (measured in watts) is equal to  10𝐼2 , where  𝐼  is the current measured in amperes. When  𝐼=6  amperes, what is the rate of change of  𝑃  with respect to  𝐼 ?

oobleck · Answer

P = I^2 R = 10I^2 dP/dI = 2I so plug in your numbers