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Homework Help: Related rates of change

  1. Dec 8, 2004 #1


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    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


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


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    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


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    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]

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