A laboratory power supply maintains a constant resistance wire at (assume the…

MATHEMATICS · Multi-part · A Level · Mathematics · Quantities and units in mechanics · Quantities and units in mechanics

Problem

A laboratory power supply maintains a constant resistance wire at

R=12.0\,\Omega

(assume the temperature of the wire is held fixed). The current through the wire is a differentiable function

I(t)

. At time

t=3.0\text{ s}

the measured current is

I=2.50\text{ A}

and is increasing at a rate of

\dfrac{dI}{dt}=0.40\text{ A\,s}^{-1}

. The voltage across the wire satisfies

V=IR

. (a) Calculate the instantaneous rate of change of the voltage,

\dfrac{dV}{dt}

, at

t=3.0\text{ s}

. Include appropriate units. (b) The electrical power dissipated in the wire is

P=IV

. Determine

\dfrac{dP}{dt}

at the same instant. Express your answer in watts per second and clearly indicate all steps in your calculation.