Calculate the time constant (RC circuit)

In summary, the time constant for the enclosed circuit diagram is calculated by using the combined resistance of the timing circuit, using the rules for the sumation of parallel and series resistances. The total resistance acting through the capacitor can be calculated using the equation R_{total} = R_{series} + \frac{1}{R_{parallel}}. The time constant during the charging process is t = RC and since there is no resistance in series with the capacitor, the time constant is zero.
  • #1
hellraiser
Hi.
How am I supposed to calculate the time constant for the enclosed circuit diagram.
I know time constant t = 1/RC
In this case do i take only one resistance or the combined value (series value)
Assume any values. I only want to understand how it is to be done.

PS: Sorry for the stupid drawing. I used MSPAINT to draw it. I think I should have practised drawing more as a kid. :)
 

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  • #2
I can't see the picture but as far as I know you use the combined resistance of the timing circuit using the rules for the sumation of parallel and series resistances.
 
  • #3
Ok i will try to draw it in ASCII.
__res______
| | |
| | |
bat cap res
| | |
|____|____|
res is resistor
cap is capacitor
bat is battery (+ve terminal up)
 
  • #4
Obviously I failed :(
 
  • #5
If I guessed right, the resistor is on the top line between the battery and the capacitor and the resistor is on the leg to the right of the capacitor??
 
  • #6
Yes. You got it right.


Why is the attachment not being cleared. It's been nearly 24 hrs since I posted it. Anyone listening?
 
  • #7
So now you calculate the total resistance of the circuit. Remember one is in parallel while the other is in series.
 
  • #8
How? Could you show me?
I know R(series) = R1 + R2
R(parallel) = 1/R1 + 1/R2
 
  • #9
Correct. You want to know the resistance acting through the capacitor. Think about it logically, if one resistor is in series with the capacitor and one is in parallel with it then could you write an equation of the total resistance acting through the circuit base on what you just said?
 
  • #10
I don't know how? Should I apply Ohm's Law and solve for an expression with time variation of current? But that would be quite lengthy.
 
  • #11
No. Simply use [tex] R_{total} = R_{series} + \frac{1}{R_{parallel}} [/tex]
 
  • #12
So the ans is R1 + R2 + (R1*R2)/(R1+R2)
 
  • #13
Ive given you the answer to calculate the total resistance above.
 
  • #14
I'm doing the same problem--how did you get that expression for Rtotal?
 
  • #15
andrewjohnsc said:
I'm doing the same problem--how did you get that expression for Rtotal?

Witchcraft or maybe prayer?:rolleyes:

Let the battery have emf Vo, and label the resistors R and r.

Answer these simple questions:

a) When Vc = 0, what is Ic?

b) When Ic = 0, what is Vc?

How long would it take the current in a) (if it stayed constant)
to charge (hint!) the capacitor C to the voltage in b)?
This is the time constant.

David
 
Last edited:
  • #16
Here's a better presented problem.
(Ignore the random stabs at answers)

Having said that, the first question should read:

1) Determine the current in each resistor and charge on the capacitor
immediately after the switch is closed


https://www.physicsforums.com/showthread.php?t=312098

In addition to what you are asked for, answer this:

What is the time constant during the charging process (switch closed)?
 
Last edited:
  • #17
Let R1 is R series and R2 is the resistance in parallel with capacitor. You can interchange R2 and C with affecting the circuit diagram. At the instant the switch is on, the voltage across R2 is E*R2/(R1 + R2). This voltage charges the capacitor. There is no resistance in series with the capacitor. Since the time constant t = RC ( not 1/RC as you have mentioned.) and R = 0 , the time constant is zero.
 

What is the Time Constant in an RC Circuit?

The time constant (\( \tau \)) in an RC circuit is a measure of how quickly the circuit's voltage or current changes in response to a step input or disturbance. It characterizes the time it takes for the voltage or current to reach approximately 63.2% (1 - 1/e) of its final steady-state value in an exponential manner.

How Can I Calculate the Time Constant (\( \tau \))?

The time constant (\( \tau \)) in an RC circuit can be calculated using the formula:

\[ \tau = R \cdot C \]

Where:

  • \( \tau \) is the time constant in seconds (s).
  • \( R \) is the resistance in ohms (Ω).
  • \( C \) is the capacitance in farads (F).

What Does the Time Constant Represent?

The time constant (\( \tau \)) represents the time it takes for the voltage or current in an RC circuit to change by approximately 63.2% from its initial value to its final steady-state value. It is a measure of the circuit's time response to changes in input or disturbances. A smaller time constant indicates a faster response, while a larger time constant implies a slower response.

What Are the Practical Applications of the Time Constant?

The time constant (\( \tau \)) has practical applications in various fields, including electronics and engineering:

1. Signal Processing:

In signal processing, the time constant is used to characterize the response time of filters and systems, helping to design and analyze their behavior.

2. Circuit Design:

Engineers use the time constant to design and analyze RC circuits, including filters, timing circuits, and voltage smoothing circuits.

3. Control Systems:

In control systems engineering, the time constant is used to assess the speed of response and stability of control loops and systems.

4. Environmental Monitoring:

The time constant can be applied to analyze environmental sensors and measurement systems, where response time is critical.

What Happens to the Voltage or Current in an RC Circuit Over Time?

In an RC circuit, the voltage or current changes over time according to an exponential decay or growth curve, depending on the type of input or disturbance. Initially, the voltage or current changes rapidly, and as time progresses, it approaches its final steady-state value. The time constant (\( \tau \)) determines the rate of this change.

How Does the Resistance (\( R \)) and Capacitance (\( C \)) Affect the Time Constant (\( \tau \))?

The resistance (\( R \)) and capacitance (\( C \)) values in an RC circuit directly affect the time constant (\( \tau \)).

1. Resistance (\( R \)):

A larger resistance (\( R \)) value results in a larger time constant (\( \tau \)), leading to a slower response of the circuit to changes in input. Conversely, a smaller resistance (\( R \)) leads to a smaller time constant and a faster response.

2. Capacitance (\( C \)):

A larger capacitance (\( C \)) value results in a larger time constant (\( \tau \)), leading to a slower response. A smaller capacitance (\( C \)) results in a smaller time constant and a faster response.

How Can I Use the Time Constant for Circuit Analysis?

When analyzing an RC circuit, you can use the time constant (\( \tau \)) to determine its time response and behavior. It helps you understand how quickly the circuit reaches its steady-state value after a change in input and can be useful for designing and optimizing circuit performance.

Additionally, you can use the time constant to calculate time-related parameters, such as the time it takes for the voltage or current to reach specific percentages of their final values or to estimate the circuit's response to different input signals.

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