1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Related rates of change

  1. Dec 8, 2004 #1


    User Avatar
    Gold Member

    Ohm's law for electrical circuits states that V=IR, where V is voltage, I is current in amperes, and R is the resistance in ohms. Suppose that V is increasing at the rate of 1 volt/sec while I is decreasing at the rate of 1/3 amp/sec. Let t denote time in seconds.
    a)what is the value of dV/dt?
    b)what is the value of dI/dt?
    c)what equation relates dR/dt to dV/dt and dI/dt?
    d)Find the rate at which R is changing when V=12 volts and I=2 amps. Is R increasing or decreasing?

    I don't think I had any problems with the first 3 parts...

    [tex]a) \frac{dV}{dt}=1 v/s[/tex]

    I don't quite understand part d. It gives information to be used in the original equation, not the differentiated one. Maybe it is irrelevant and I just need to do this? :

    [tex]\frac{dR}{dt}=-3 ohms/s[/tex]

    If someone could help me quickly I would appreciate it!!
  2. jcsd
  3. Dec 8, 2004 #2
    Why don't you need to use the product rule to differentiate the RHS? I would have thought it should be dV/dt = d(IR)/dt = RdI/dt + IdR/dt.
  4. Dec 8, 2004 #3


    User Avatar
    Gold Member

    You're right, slipped my mind, Thanks.
  5. Dec 8, 2004 #4


    User Avatar
    Science Advisor
    Homework Helper

    Well,Nylex,you're right...Again.He should be differentiating Ohm's law wrt ti time and substitute all known quantities in the new equation and from there to extract dR/dt.

    Let's hope he sees his mistake.

  6. Dec 8, 2004 #5


    User Avatar
    Gold Member

    Yes, I understand my mistake. I had a very similar problem earlier in the homework and did it correctly, the time pressure just made me think a little too fast. When he pointed out I differentiated it incorrectly, I checked my work and realized you actually don't even use product rule, but rather quotient rule since it asks for dR/dt in relation to the others, you need to solve for R then differentiate:


    substituting in numbers:


    [tex]\frac{dR}{dt}=\frac{6}{4}=1.5 ohms/s[/tex]

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Related rates of change
  1. Rate of change (Replies: 9)

  2. Changing rates (Replies: 12)

  3. Rate of change (Replies: 5)

  4. Rate of change (Replies: 2)