Question

the voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. the resistance R is slowly increasing as the resistor heats up. Use Ohm's Law, V=IR to find how the current I is changing at the moment when R=400 ohms, I=0.08A, dV/dt=-0.01 Volts/sec, and dR/dt=0.03 Ohms/sec

Answer 1

mm thats a good question actually

Answer 2

rearrange to get I = V/R

Answer 3

then you need to apply quotient rule to find the derivative, since both V and R are functions of time

Answer 4

u=V
du/dt = dV/dt

m= R
dm/dt = dR/dt

Answer 5

\[\frac{dI}{dt} = \frac{ R \frac{dV}{dt} - V \frac {dR}{dt} } { R^2} \]by qoutinet rule

Answer 6

now we have a value for R and I , we can find the value of V by ohms ( even though ohms law is not 100% valid as the temperature is not constant ) , nevertheless

V= 400 x 0.08 = 32

Answer 7

then you have all the values, sub them in, get a calculator