Question

The Power in a circuit is given by the formula P=I^{2}R, where I is the Current and R is the Resistance. If the Resistance is always constant at 500, the Current is 1, and dI/dt = -0.5, then dP/dt = -500.

True or false and please show work. Thank you

Answer 1

True

Explanation:

`P(t) = I^2(t)R`

Taking the derivative of P(t) with respect to time,

`(dP(t))/(dt) = 2I(t)(dI(t))/(dt)R`

`\:\:\:\:\:\:\:\:= 2(1)(-0.5)(500) = -500`