Unraveling the Mystery of Current: Expressing F in Seconds and Ohms

AI Thread Summary
The discussion focuses on expressing capacitance in Farads in terms of seconds and Ohms within the context of an RC circuit. The user initially struggles with the mathematical manipulation involving current, resistance, and capacitance. They mistakenly conclude that Farads equal zero due to an error in their logarithmic calculations. Clarification is provided that, when considering the relationship between charge, time, and resistance, an Ohm-Farad indeed has the dimension of time. Ultimately, the user gains understanding of the dimensional analysis and the nature of the equations involved.
nate92488
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I have this problem I just can't figure out.

Current = A (Ampere)

i(t)=z(e^t/(RC))

where z is the initial current at t=0, R is the resistance in Ohms and C is the capacitance expressed in secondary units as F (Farad)

- Express the units of F in terms of seconds and ohms

So, this is what I tried to do, tell me where I went wrong

A = A e^(s/F-Ohms)

1 = e^(s/F-Ohms)

ln(1) = s/F-Ohms

0 = s/F-Ohms

F = 0

I obviously did something wrong, so any help would be apreciated, thank you!
 
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If you think of an RC circuit as a second order differential equation you will see

dQ/dT + 1/(R*C)*Q = Junk

Where junk = 0 for a loop of a circuit without any external components. Otherwise it can also be some forcing function driven by batteries, power sources, etc. But anyways, Q is the charge here so...

dQ/dT = charge/time (amps)

thus Q*1/(R*C) = charge/time since Q = charge, R*C has dimension [T]

Thus an Ohm-Farad has dimension [T] and the quantity in the exponent in your equation is dimensionless then - as it should be
 
thank you, I got it now.
 
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