For the circuit shown in the figure, the switch S is initially open and the capacitor is…
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Question “For the circuit shown in the figure, the switch S is initially open and the capacitor is…”
For the circuit shown in the figure, the switch S is initially open and the capacitor is uncharged.
The switch is then closed at time t = 0. How many seconds after closing the switch will the
energy stored in the capacitor be equal to 50.2 mJ?
Answer
This problem can be solved using the following concepts: maximum charge on a capacitor within an RC Circuit, charge as a function time in an RCC circuit, and energy inside a charged capacitor.
To find the energy stored within a capacitor, first use the relationship between charge and time as a function.
Next, calculate the relationship between voltage and capacitance to determine the maximum charge for a capacitor.
Finally, you can use charge as a function time in an RCC circuit to determine how long it takes for a capacitor to store
![50.2 m)](https://drive.google.com/uc?id=1G9JQdrwM7O2QcFmZNHwz57g_OSgMtL46&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
electricity.
After the switch is closed the capacitor connects to the battery. The charge is then stored in the capacitor.
Charge as a function time is the expression
![Q=0[1-ewt](https://drive.google.com/uc?id=1_gbQ5o7Ne62B1BBnN81yswx7iaXl3bdf&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
Here, time is
![](https://drive.google.com/uc?id=1zEJ00WS17oSR_pxDBULuAfyc3I_-ov4a&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
and resistance is
![](https://drive.google.com/uc?id=1PJ9XER0rLVv_wdLtcSog7AtOkDXzkLxC&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
. Capacitance is
![](https://drive.google.com/uc?id=1OMyxNKcwyVXZQw-_atBwJBTICL8ZXEi_&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
. Maximum charge on the capacitor:
![](https://drive.google.com/uc?id=1ldb58ZM9XmmdXeWKT2s-IajWkKT86A1Q&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
. Charge as a function time is
![](https://drive.google.com/uc?id=16mFkEoc9hDE7ROnlqmgD-6QfyueR-4IN&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
.
The energy stored in the capacitor’s capacitor is described as
![](https://drive.google.com/uc?id=17dxeTpUy0V3rYyBe-_u5p1MmC7_iU-wc&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
The maximum charge for a capacitor is
![Q = CV](https://drive.google.com/uc?id=1cwVgGwzcV-cvSGrVEh4XmhIlQaT8j8h0&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=13OGGlODp7KDeszIp6o7q1WpF2mbSZf-u&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
.
The energy stored in the capacitor’s capacitor is described as
![](https://drive.google.com/uc?id=17dxeTpUy0V3rYyBe-_u5p1MmC7_iU-wc&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
Modifying the charge expression is
![Q=2CU](https://drive.google.com/uc?id=1kW-wH_7YVFbDTf9IlOl9L04Wi8YJGJqo&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
Substitute HTMLmedia_tag_12$ to and HTMLmedia_tag_14$ to .
![0-929/P)02
=v2(90x10°F)(50.2x10*)
)
=3x108c](https://drive.google.com/uc?id=1HgRIckgJKiihANCPussMkFnGxqgp10Z-&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
The maximum charge for a capacitor is
![Q = CV](https://drive.google.com/uc?id=1cwVgGwzcV-cvSGrVEh4XmhIlQaT8j8h0&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
Substitute HTMLmedia_tag_18$ to and HTMLmedia_tag_20$ to .
![2. =(90ur(1059) (cov)
=(90x106F)(400)
= 3.6x10°C](https://drive.google.com/uc?id=1RrxwgmbOHV8zD48fB3RElS8mPE1pHhjJ&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
The charge is a function time.
![Q=0[1-ewt](https://drive.google.com/uc?id=1_gbQ5o7Ne62B1BBnN81yswx7iaXl3bdf&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
Modifying the expression
![-0
151](https://drive.google.com/uc?id=1zG9jMu9QIqe7zBN4c9x3Pgbir_692xvs&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
Place a log of natural wood on each side.
![In exc = in(.)
le-
1=(RC)Inc.](https://drive.google.com/uc?id=1-3q0Ou5bZbUPQJBF8WLLdL4_bkGOzWdj&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
Substitute
![3.6x10°C](https://drive.google.com/uc?id=1BaiA0DmsLoBJMSmj2i06W0BrHyCUBv0s&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
to
![](https://drive.google.com/uc?id=1kz_T8oHLzTkuKObnH-VHVJyt5pf5LQjm&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
;
![](https://drive.google.com/uc?id=1a4dzYPcdkeQomZCGZQucdJ0sKbQW9Mvc&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
to
![](https://drive.google.com/uc?id=11lE9Vlrw5rL7I7uinM-QeIbOg_vQW2O1&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
;
![0.50 ΜΩ](https://drive.google.com/uc?id=1GM4kI7G48ol-trcgGdLKiMNHO-3bJR4F&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
to
![](https://drive.google.com/uc?id=1PysyVRu7xT2SjPJgMKp14B30xDhRucd6&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
;
![3x10-C](https://drive.google.com/uc?id=1Ao2RdHq6Nzy8imRmZ62dmsqMOW8AEeNW&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
to
![](https://drive.google.com/uc?id=1Jftew_PSh8wGzU9QwXK7dS-y_dgfh3X9&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
.
![3.6x10-C
-=[0.50m1/ 10Msa) (90F(10° uf)(3.6–10°C)-(3x10°c))
= (0.50x10^92(90x10“F)in (6)
= 80.629s
81s](https://drive.google.com/uc?id=1aZbTvDArP9GGGung9m2gAiZC5H2UYcth&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
Ans:
The time it takes for a capacitor to store
![50.2 m)](https://drive.google.com/uc?id=1iZPku_Np8zAqrFXRPC7SH-qaPC71-Elz&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
electricity is over when the switch closes. It costs
![](https://drive.google.com/uc?id=1aoXoeRjIpLh9HASVPQgvBPZ4_YWMv2DV&export=download/For-the-circuit-shown-in-the-figure,-the-switch-S is-initially-open-and-the-capacitor-is.png?x-oss-process=image/resize,w_560/format,webp)
.
Conclusion
Above is the solution for “For the circuit shown in the figure, the switch S is initially open and the capacitor is…“. We hope that you find a good answer and gain the knowledge about this topic of science.