In an electric circuit

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

In an electric circuit, the instantaneous power delivered to a resistor is modeled by

P=I^{2}R

, where

P

is measured in watts (W),

I

is the current in amperes (A), and

R

is the resistance in ohms (Ω). At a particular moment the current through the resistor is

I=3.00\text{ A}

and is increasing at a rate of

\dfrac{dI}{dt}=0.150\text{ A/s}

. Because the resistor is heating, its resistance is also changing:

R=8.00\,\Omega

and

\dfrac{dR}{dt}=0.050\,\Omega/\text{s}

at that same instant. (a) Obtain a formula for

\dfrac{dP}{dt}

expressed in terms of

I,\,\dfrac{dI}{dt},\,R

, and

\dfrac{dR}{dt}

. (b) Compute

\dfrac{dP}{dt}

using the values provided, and interpret the physical meaning of the sign and units of your result.