Science desk
< September 28	<< Aug \| September \| Oct >>	Current desk >

Welcome to the Wikipedia Science Reference Desk Archives
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

September 29

Capacitor connected by a single terminal

If I initially short both terminals of a capacitor to ground for a short time, then connect one of them to the + terminal of a battery through a resistor, would I have a transient current the time for the electron defect on the + terminal to transfer to the capacitor? Malypaet (talk) 22:06, 29 September 2022 (UTC)[reply]

Yes. A current starts immediately

I_start = V_battery / R_resistance

where V_battery is the voltage on the battery + terminal (that may be described as a deficit of electrons relative to the - terminal that we assume you have grounded, the same as the unmentioned capacitor terminal). The transient current decays towards zero, falling by

1 / e \approx 36.8%

of its strength in every time interval of RC seconds. This is called the time constant of the circuit. See Time_constant#Time_constants_in_electrical_circuits and Rise_time#One-stage_low-pass_RC_network. Philvoids (talk) 11:05, 30 September 2022 (UTC)[reply]

@Philvoids and Malypaet: That answer doesn't seem complete. Although it is technically correct, it misses one detail: the question is

If I initially short both terminals of a capacitor (...), then connect one of them to the + terminal of a battery through a resistor, (...)

So we have a circuit made of a battery V, a resistor R, a capacitor C and a negligible capacity C₀ of an opened break between the other terminal of the capactior and the '–' terminal of the battery. So the time constant of the exponential fall of the current will be less than RC₀, which is orders of magnitute smaller than just RC. --CiaPan (talk) 08:08, 2 October 2022 (UTC)[reply]

@CiaPan The doubt that you introduce to the OPs question is clearer when the part is properly quoted:

If I initially short both terminals of a capacitor for a short time, then connect one of them to the + terminal of a battery through a resistor, (...) (with my bolding)

The OPs phrasing leaves unspecified what is done with the other terminal of the capacitor. My answer responds by pointing out the reasonable assumption:

(..)we assume you have grounded (...) the unmentioned capacitor terminal.

I stand by my answer given. I do not endorse introducing vague intangibles that can reflect self-indulgent thinking, such as a notion of a "negligible capacity of an opened break", particularly when you proceed to calculate the relative magnitude of the "negligible" capacity and assert that is the circuit we have. In a pursuit of elaboration a misguided person may further insist that without the non-zero equivalent series inductances and resistances that all practical capacitors, batteries and connecting wires have, any answer is incomplete. That critique is unhelpful here. Philvoids (talk) 11:20, 2 October 2022 (UTC)[reply]

Philvoids: I did not introduce any doubt, I just read the description: ″I (...) short both terminals (...) to ground for a short time″ – it's quite obvious that after a short time both terminals got disconnected from ground. Then ″(I) connect one of them to (...) battery″ – nothing is said to happen to the other terminal, so after disconnecting from ground it remains open. The end. My comment follows precisely what has been asked. --CiaPan (talk) 08:47, 3 October 2022 (UTC)[reply]
P.S. A plain text like '@CiaPan' does not do whan you mean. You need to link to a user page to make a notification, as described at Help:Notifications. CiaPan (talk)

Is the other end of the capacitor connected to the negative terminal of the battery? Graeme Bartlett (talk) 10:20, 2 October 2022 (UTC)[reply]

The other terminal of the capacitor is not connected, like write CiaPan. Malypaet (talk) 21:16, 2 October 2022 (UTC)[reply]

                      10,000 ohm
 +---o      o---------/\/\/\/\-----+
 |    \                  R         |
 |     \    SPDT switch            |                              no connection
 |      \                          |                  +-------o   o
 |       o                       _____+10V            |        \
 |       |                         -   battery      _____       \
 |    +_____                       :                |    |      :\
 |     |   |                     _____              _____  C    : o---+                  battery
 |     _____  C                    -                |    |      :     |                + |   |
 |     |xxx|  100 µF               |                  |         :     |         R        ||  ||    
 |       |                         |                  +-------o :  o--|------/\/\/\/\----||..||----+
 |       |                         |                           \:     |                  ||  ||    |
 |    + / \                        |                            \     |                  |   |     |
 |     /   \ 1 mA F.S.D.           |                      DPDT   \    |                            |
 |    (  A  )                      |                     switch   o---+                            |
 |     \   /                       |                                  |                          _____
 |      \ /                        |                                  |                           ___
 |       |                         |                                  |                            _
 +_______+_________________________+                                _____
                  |                                                  ___
                _____                                                 _
                 ___
                  _
                      CIRCUIT A                                    CIRCUIT B

Circuit A can be constructed with the component values shown and includes a milliammeter. Throw the switch and it rewards by display of a current decaying with 1-second time constant. After the OP confirmed CiaPan's interpretation of their question, I think we are left with Circuit B in which I keep the battery negative grounded. However I don't see it leading to a practical or instructive demonstration. Philvoids (talk) 11:59, 4 October 2022 (UTC)[reply]