How Do You Calculate Time Constant and Capacitance in an RC Circuit?

AI Thread Summary
To calculate the time constant and capacitance in an RC circuit, the time constant is defined as the product of resistance (R) and capacitance (C). The initial current can be determined using the equation I = E/R, leading to an initial current of 4.4 mA. The current at a later time can be expressed using the equation I = I0e^(-t/RC), which allows for the calculation of capacitance. A calculated capacitance of 7.48 µF was reported, but confusion arose regarding whether the value could be negative, as capacitance must always be a positive value. The discussion emphasizes the importance of correctly applying the equations and understanding the physical implications of the results.
Obsqura
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Homework Statement



A battery with emf = 2V is connected to a RC circuit with a 450Ω resistor and an unknown capacitor. After 3.8 milliseconds, the current is 2.2mA.

(a) Find the time constant and the capacitance.

(b) Now, 2.9 ms after the charging begins, find the current I, the charge q at the capacitor and the rate of resistor heating P.


Homework Equations


time constant = RC
I = E/(R + r)
Q = CE
V = IR
P = (I^2)R


The Attempt at a Solution



I haven't even started on b yet, since I cannot even figure out part a. I flipped through my textbook, but haven't seen any other relevant equations where I can plug the numbers into find the time constant and capacitance so any help is welcome. Thanks.
 
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You'll need to find the time constant first, and then from that, find the capacitance.

To find the time constant, look for an equation that tells you how the current changes over time. You're given some information about the value of the current at a particular time, and you can also use some physical reasoning to figure out the value of the current at the initial time, t=0, when charging begins. (Hint: what is the effect of the capacitor at t=0?) Then you can use the current-time equation you find to compute the value of the time constant.
 
Okay, thanks. Does this sound about right?

I used equation i = E/R at time 0 to get i = 4.4 * 10^-3.

Then used the equation i = I0e^(-t/RC) and solved for C.
I used what was given at the new time and the I0 that I solved for to get:

0.0022A = 4.4*10^-3A e^(-0.0038s/450ΩC)

I then solved for C and got 7.48*10^-6 F. Does that sound about right?

But the final answer was negative for C. Does it supposed to be negative? Thanks for the help.
 
Obsqura said:
But the final answer was negative for C. Does it supposed to be negative? Thanks for the help.
But you just said you got 7.48*10^-6 F. Which is it, positive or negative?

If it's negative, does it make sense to have a negative capacitance?
 
As far as I know, it cannot be negative. I just wanted to make sure I solved it correctly.
 
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