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

In summary, the time constant was found using the equation i = I0e^(-t/RC). A value for the initial current was determined through physical reasoning, and then substituted into the equation along with the given information at a later time to solve for the capacitance. The final answer for the capacitance was found to be 7.48*10^-6 F. There is no indication that the capacitance should be negative.
  • #1
Obsqura
4
0

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.
 
Physics news on Phys.org
  • #2
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.
 
  • #3
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.
 
  • #4
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?
 
  • #5
As far as I know, it cannot be negative. I just wanted to make sure I solved it correctly.
 

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

1. What is a time constant in relation to capacitance?

A time constant is a measure of how quickly a capacitor charges or discharges in an electrical circuit. It is determined by the product of the capacitance value and the resistance in the circuit, and it represents the time it takes for the capacitor to reach 63.2% of its maximum charge or discharge.

2. How is the time constant calculated?

The time constant, denoted by the symbol τ (tau), is calculated by multiplying the capacitance (C) in farads by the resistance (R) in ohms. The formula is τ = RC, where R is the resistance and C is the capacitance.

3. What is the relationship between time constant and capacitance?

The time constant is directly proportional to the capacitance. This means that as the capacitance increases, the time constant also increases. Similarly, if the capacitance decreases, the time constant decreases as well.

4. How does the time constant affect the charging and discharging of a capacitor?

The time constant determines the rate at which a capacitor charges and discharges. A larger time constant means that the capacitor charges and discharges more slowly, while a smaller time constant results in a faster charging and discharging process.

5. What is the significance of time constant and capacitance in circuit design?

The time constant and capacitance are important considerations in circuit design as they affect the behavior of capacitors in a circuit. They determine how long it takes for a capacitor to charge or discharge, and can also impact the stability and performance of the circuit. Therefore, it is important to carefully select the values of capacitance and resistance in a circuit to achieve the desired time constant and overall function of the circuit.

Similar threads

Capacitor circuit time constant problem
Replies
2
Views
2K
Time constant for parallel RC circuit
Replies
2
Views
1K
Opamp RC-circuit -- Capacitor time constant calculation
Replies
6
Views
3K
Investigating Voltage, Capacitance & Resonance in DC/AC Circuits
Replies
1
Views
2K
Changing capacitance effect on ripple in full rectification circuit
Replies
4
Views
2K
Calculating Charge and Time in a Discharging RC Circuit
Replies
3
Views
1K
How Long Does It Take for a Capacitor to Charge to 8V in an RC Circuit?
Replies
2
Views
1K
Finding R(t) in discharging RC circuit
Replies
4
Views
1K
Why can we add impedances in series?
Replies
4
Views
688
Time Constant ≠ Time constant from experiment
Replies
9
Views
10K

Hot Threads

Recent Insights

Back
Top