Question

The power P (watts) of an electric circuit is related to the circuit's resistance R (ohms) and current I (amperes) by the equation P=RI^2.
b) How is dR/dt related to dI/dt if P is constant?

Answer 1

Take your derivative

\[\large \frac{dP}{dt} = (I^2\frac{dR}{dt}) + (2RI \frac{dI}{dt})\]

If P is constant...we know dP/dt will = 0 so

\[\large I^2\frac{dR}{dt} + 2RI\frac{dI}{dt} = 0\]

Now just solve for \(\large \frac{dR}{dt}\)

Answer 2

awesome, thanks! :)