# Rates of change question

• April 25th 2013, 11:40 PM
Vishak
Rates of change question
Could someone please get me started on this question, I have no idea where to begin. Thanks heaps.

If two resistors with resistances R1 and R2 are connected in parallel, then the total resistance R, measured in ohms is given by:

1/R = 1/R1 + 1/R2

If R1 and R2 are increasing at rates of 0.9/s and 0.5/s respectively, how fast is R changing when R1 = 50 and R2 = 115?
• April 25th 2013, 11:52 PM
MarkFL
Re: Rates of change question
Have you tried implicitly differentiating with respect to time $t$?
• April 25th 2013, 11:59 PM
Vishak
Re: Rates of change question
How should I go about doing that with three variables - R, R1 and R2 ?
• April 26th 2013, 12:01 AM
MarkFL
Re: Rates of change question
All three variables for functions of time, so use implicit differentiation...i.e., the chain rule.
• April 26th 2013, 12:11 AM
Vishak
Re: Rates of change question
I'm not sure whether I've done this correctly, but heres my attempt at that:

Differentiating with respect to t -

(-R-2)dR/dt = (-R1)-2dR1/dt - (R2)-2dR2/dt

and then solving for dR/dt i got 0.483.
• April 26th 2013, 12:19 AM
MarkFL
Re: Rates of change question
Yes, I get the same result (5261/10890) Ω/s...good work! :D
• April 26th 2013, 12:22 AM
Vishak
Re: Rates of change question
Yay! Thanks heaps mate :)