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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]

[tex]b)\frac{dI}{dt}=-\frac{1}{3}amp/sec[/tex]

[tex]c)\frac{dV}{dt}=(\frac{dI}{dt})(\frac{dR}{dt})[/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{dV}{dt}=(\frac{dI}{dt})(\frac{dR}{dt})[/tex]

[tex]1v/s=(-\frac{1}{3})(\frac{dR}{dt})[/tex]

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

If someone could help me quickly I would appreciate it!!

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# Homework Help: Related rates of change

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