Expressing farad units in terms of seconds and ohms

[nate92488]

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!

 

[DLinkage]

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

 

[nate92488]

thank you, I got it now.