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

In summary, the conversation discusses the units of capacitance (F) in an RC circuit, where F is expressed in terms of seconds and ohms. The conversation also mentions a second order differential equation and the dimensions of Q and R*C.
  • #1
nate92488
2
0
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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  • #2
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
 
  • #3
thank you, I got it now.
 

What is current?

Current is the flow of electric charge, typically measured in units of amperes (A).

How is current expressed in seconds?

Current cannot be directly expressed in seconds, as it is a measure of charge flow over time. However, the unit of time can be a factor in calculating current, for example, dividing charge (C) by time (s) to get current (A).

What is the relationship between current and resistance?

The relationship between current and resistance is described by Ohm's Law, which states that the current through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance between them.

What are the units for measuring current and resistance?

Current is measured in amperes (A), while resistance is measured in ohms (Ω).

How do you calculate current given resistance and voltage?

To calculate current (I) given resistance (R) and voltage (V), you can use Ohm's Law: I = V/R. Alternatively, you can rearrange the formula to solve for current: I = V/R.

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