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Question:
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!
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!