Expert: Abe Mantell - 1/4/2012

Question
Part of a circuit has two resistors connected in parallel. R1 is a constant resistor of 10 ohm, while R2  is a variable resistor with resistance that varies at a rate of 2 ohms per minute. The total, or effective, resistance, R, provided by this circuit is given by:
1/R = 1/R1 + 1/R2
At what rate does the effective resistance change when R @ is 100 ohms? Round off your answer to four decimal places.

Answer
Hello Maria,

In this case, I would solve for R in terms of R1 and R2, then differentiate with respect to t.

Solving for R gives: R=(R1*R2)/(R1+R2), now let R1=10, so R=(10*R2)/(10+R2)

Now differentiate wrt to t:
dR/dt=[10*R2'*(10+R2)-10*R2*R2']/(10+R2)^2
= 100*R2'/(10+R2)^2

Now solve for R2 when R=100 so we can substitute into dR/dt.
100=(10*R2)/(10+R2) ==> This gives R2=-100/9...so I think the problem should be for
when R2=100, not R=100.  Using R2=100 with dR2/dt=2 gives:
dR/dt=100*2/(10+100)^2=200/110^2=2/121 ohms/min

I hope this helps.

Abe