# Calculate the time constant (RC circuit)

1. Feb 3, 2006

### 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. Feb 4, 2006

### Hootenanny

Staff Emeritus
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. Feb 4, 2006

### hellraiser

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. Feb 4, 2006

### hellraiser

Obviously I failed :(

5. Feb 4, 2006

### Hootenanny

Staff Emeritus
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. Feb 4, 2006

### hellraiser

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. Feb 5, 2006

### Hootenanny

Staff Emeritus
So now you calculate the total resistance of the circuit. Remember one is in parallel while the other is in series.

8. Feb 5, 2006

### hellraiser

How? Could you show me?
I know R(series) = R1 + R2
R(parallel) = 1/R1 + 1/R2

9. Feb 5, 2006

### Hootenanny

Staff Emeritus
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. Feb 6, 2006

### hellraiser

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. Feb 6, 2006

### Hootenanny

Staff Emeritus
No. Simply use $$R_{total} = R_{series} + \frac{1}{R_{parallel}}$$

12. Feb 6, 2006

### hellraiser

So the ans is R1 + R2 + (R1*R2)/(R1+R2)

13. Feb 6, 2006

### Hootenanny

Staff Emeritus
Ive given you the answer to calculate the total resistance above.

14. May 5, 2009

### andrewjohnsc

I'm doing the same problem--how did you get that expression for Rtotal?

15. May 6, 2009

### davieddy

Witchcraft or maybe prayer?

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: May 6, 2009
16. May 6, 2009

### davieddy

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