-->[Author ID0: at Thu Nov 30 01:06:00 1899 ] CYGA[Author ID1: at Wed Nov 11 11:11:00 1998 ]N SEBASTIAN[Author ID1: at Wed Nov 11 11:11:00 1998 ][Author ID0: at Thu Nov 30 00:00:00 1899 ] [Author ID0: at Thu Nov 30 00:00:00 1899 ] FIEDOR MARCIN[Author ID1: at Wed Nov 11 11:14:00 1998 ] [Author ID1: at Wed Nov 11 11:11:00 1998 ][Author ID0: at Thu Nov 30 00:00:00 1899 ] KIRC GRZEGORZ[Author ID1: at Wed Nov 11 11:15:00 1998 ][Author ID1: at Wed Nov 11 11:09:00 1998 ]N[Author ID1: at Wed Nov 11 11:09:00 1998 ]i[Author ID1: at Wed Nov 11 11:09:00 1998 ]z[Author ID1: at Wed Nov 11 11:09:00 1998 ]i[Author ID1: at Wed Nov 11 11:09:00 1998 ]e[Author ID1: at Wed Nov 11 11:09:00 1998 ]l[Author ID1: at Wed Nov 11 11:09:00 1998 ]s[Author ID1: at Wed Nov 11 11:09:00 1998 ]k[Author ID1: at Wed Nov 11 11:09:00 1998 ]i[Author ID1: at Wed Nov 11 11:09:00 1998 ] [Author ID1: at Wed Nov 11 11:09:00 1998 ]R[Author ID1: at Wed Nov 11 11:09:00 1998 ]o[Author ID1: at Wed Nov 11 11:09:00 1998 ]b[Author ID1: at Wed Nov 11 11:09:00 1998 ]e[Author ID1: at Wed Nov 11 11:09:00 1998 ]r[Author ID1: at Wed Nov 11 11:09:00 1998 ]t[Author ID1: at Wed Nov 11 11:09:00 1998 ][Author ID0: at Thu Nov 30 00:00:00 1899 ] P[Author ID1: at Wed Nov 11 11:09:00 1998 ]i[Author ID1: at Wed Nov 11 11:09:00 1998 ]s[Author ID1: at Wed Nov 11 11:09:00 1998 ]k[Author ID1: at Wed Nov 11 11:09:00 1998 ]u[Author ID1: at Wed Nov 11 11:09:00 1998 ]r[Author ID1: at Wed Nov 11 11:09:00 1998 ] [Author ID1: at Wed Nov 11 11:09:00 1998 ]M[Author ID1: at Wed Nov 11 11:09:00 1998 ]a[Author ID1: at Wed Nov 11 11:09:00 1998 ]r[Author ID1: at Wed Nov 11 11:09:00 1998 ]e[Author ID1: at Wed Nov 11 11:09:00 1998 ]k[Author ID1: at Wed Nov 11 11:09:00 1998 ][Author ID0: at Thu Nov 30 00:00:00 1899 ] Ordon Rafał

-->ED II[Author ID0: at Thu Nov 30 01:06:00 1899 ] L 01-->5[Author ID1: at Wed Nov 11 11:11:00 1998 ][Author ID1: at Wed Nov 11 11:13:00 1998 ]

SPRAWOZDANIE nr 1

Temat:

Sygnały w obwodzie RCL[Author ID1: at Wed Nov 11 11:20:00 1998 ] - wymuszenie skokowe .

[Author ID1: at Wed Nov 11 11:20:00 1998 ]Schemat pomiarowy:

[Author ID0: at Thu Nov 30 00:00:00 1899 ]

Równania charakterystyczne układu (po zamknięciu klucza):

[Author ID1: at Wed Nov 11 11:30:00 1998 ][Author ID1: at Wed Nov 11 11:27:00 1998 ][Author ID1: at Wed Nov 11 11:27:00 1998 ][Author ID1: at Wed Nov 11 11:27:00 1998 ][Author ID1: at Wed Nov 11 11:27:00 1998 ][Author ID1: at Wed Nov 11 11:27:00 1998 ]
[Author ID1: at Wed Nov 11 11:27:00 1998 ][Author ID0: at Thu Nov 30 00:00:00 1899 ]

[Author ID1: at Wed Nov 11 11:22:00 1998 ]
[Author ID1: at Wed Nov 11 11:22:00 1998 ]la wymuszenia napięciem stałym E mamy równanie obwodu w postaci: E = u[Author ID1: at Sun Nov 8 12:31:00 1998 ]U[Author ID1: at Sun Nov 8 12:31:00 1998 ]R(t) + u[Author ID1: at Sun Nov 8 12:31:00 1998 ]U[Author ID1: at Sun Nov 8 12:31:00 1998 ]L[Author ID1: at Wed Nov 11 11:30:00 1998 ]C(([Author ID1: at Wed Nov 11 11:30:00 1998 ]t[Author ID1: at Wed Nov 11 11:30:00 1998 ]t),

czyli po podstawieniu spadków napięć na poszczególnych elementach do powyższego wzoru otrzymamy równanie różniczkowe I rzędu:

[Author ID1: at Sun Nov 8 12:17:00 1998 ][Author ID1: at Sun Nov 8 12:17:00 1998 ]
[Author ID1: at Sun Nov 8 12:17:00 1998 ]- równanie uzależnimy od napięcia na kondensatorze, czyli[Author ID1: at Sun Nov 8 12:17:00 1998 ]:[Author ID1: at Sun Nov 8 12:17:00 1998 ]

[Author ID1: at Sun Nov 8 12:17:00 1998 ][Author ID1: at Sun Nov 8 12:17:00 1998 ][Author ID1: at Sun Nov 8 12:17:00 1998 ]
[Author ID1: at Sun Nov 8 12:17:00 1998 ][Author ID1: at Sun Nov 8 12:17:00 1998 ]

Równanie ma postać:[Author ID1: at Sun Nov 8 12:32:00 1998 ] [Author ID1: at Sun Nov 8 12:33:00 1998 ]
,[Author ID1: at Sun Nov 8 12:23:00 1998 ][Author ID0: at Thu Nov 30 00:00:00 1899 ]

[Author ID1: at Sun Nov 8 12:23:00 1998 ]

[Author ID1: at Sun Nov 8 12:26:00 1998 ]Cz[Author ID1: at Sun Nov 8 12:23:00 1998 ]N[Author ID1: at Sun Nov 8 12:25:00 1998 ]yli[Author ID0: at Thu Nov 30 00:00:00 1899 ]

n[Author ID1: at Sun Nov 8 12:25:00 1998 ]apięcie [Author ID1: at Wed Nov 11 11:37:00 1998 ]na [Author ID1: at Wed Nov 11 11:36:00 1998 ]kondensatorze:cewce:[Author ID1: at Wed Nov 11 11:35:00 1998 ] U[Author ID1: at Sun Nov 8 12:24:00 1998 ]i[Author ID1: at Sun Nov 8 12:25:00 1998 ]CL[Author ID1: at Wed Nov 11 11:35:00 1998 ] = U[Author ID1: at Sun Nov 8 12:26:00 1998 ]i[Author ID1: at Sun Nov 8 12:26:00 1998 ]CL[Author ID1: at Wed Nov 11 11:35:00 1998 ]ustalona + U[Author ID1: at Sun Nov 8 12:26:00 1998 ]i[Author ID1: at Sun Nov 8 12:26:00 1998 ]CL[Author ID1: at Wed Nov 11 11:36:00 1998 ]przejściowa

gdzie:

i[Author ID1: at Sun Nov 8 12:26:00 1998 ]U[Author ID1: at Sun Nov 8 12:26:00 1998 ]CL[Author ID1: at Wed Nov 11 11:39:00 1998 ]u[Author ID1: at Wed Nov 11 11:39:00 1998 ]u = =[Author ID1: at Wed Nov 11 11:39:00 1998 ]E

Składową przejściową prądu[Author ID1: at Wed Nov 11 11:37:00 1998 ]napięcia obliczamy z równania charakterystycznego:

podstawiając za i[Author ID1: at Wed Nov 11 11:43:00 1998 ]u_CL[Author ID1: at Wed Nov 11 11:43:00 1998 ]_p(t) = Aest i jednocześnie różniczkując powyższe równanie otrzymamy:

z którego wynika, że:

K[Author ID1: at Wed Nov 11 11:50:00 1998 ]Zorzystając [Author ID1: at Wed Nov 11 11:51:00 1998 ] [Author ID1: at Wed Nov 11 11:52:00 1998 ]z[Author ID1: at Wed Nov 11 11:51:00 1998 ] [Author ID1: at Wed Nov 11 11:52:00 1998 ] warunków [Author ID1: at Wed Nov 11 11:51:00 1998 ] [Author ID1: at Wed Nov 11 11:52:00 1998 ]początkowych[Author ID1: at Wed Nov 11 11:51:00 1998 ] [Author ID1: at Wed Nov 11 11:52:00 1998 ] i[Author ID1: at Wed Nov 11 11:51:00 1998 ] [Author ID1: at Wed Nov 11 11:52:00 1998 ] [Author ID1: at Wed Nov 11 11:47:00 1998 ] [Author ID1: at Wed Nov 11 11:56:00 1998 ] [Author ID1: at Wed Nov 11 11:47:00 1998 ]użyciem drugiegopierwszego [Author ID1: at Wed Nov 11 11:47:00 1998 ] prawa kk[Author ID1: at Wed Nov 11 11:58:00 1998 ]omutacji [ U[Author ID1: at Sun Nov 8 12:31:00 1998 ]_C(0^-) = U[Author ID1: at Sun Nov 8 12:31:00 1998 ]_C(: [Author ID1: at Wed Nov 11 11:57:00 1998 ] i[Author ID1: at Wed Nov 11 11:57:00 1998 ]_L[Author ID1: at Wed Nov 11 11:57:00 1998 ](0^-) =i[Author ID1: at Wed Nov 11 11:57:00 1998 ]_L[Author ID1: at Wed Nov 11 12:01:00 1998 ]([Author ID1: at Wed Nov 11 11:59:00 1998 ]0⁺)][Author ID0: at Thu Nov 30 00:00:00 1899 ]

[Author ID0: at Thu Nov 30 00:00:00 1899 ]

gdzie:p[Author ID1: at Wed Nov 11 11:48:00 1998 ]rzy [Author ID1: at Wed Nov 11 11:48:00 1998 ] czym:[Author ID1: at Wed Nov 11 11:48:00 1998 ] [Author ID1: at Wed Nov 11 11:56:00 1998 ] [Author ID1: at Wed Nov 11 11:59:00 1998 ]i[Author ID1: at Wed Nov 11 11:56:00 1998 ]_L[Author ID1: at Wed Nov 11 11:56:00 1998 ](0^-) = 0 [A[Author ID1: at Wed Nov 11 11:56:00 1998 ]]

U[Author ID1: at Sun Nov 8 12:30:00 1998 ]_C(0^-) = 0 [V]

oraz:[Author ID0: at Thu Nov 30 00:00:00 1899 ]

możemy otrzymać szukany parametr A :

[Author ID0: at Thu Nov 30 00:00:00 1899 ]

A= - E

[Author ID0: at Thu Nov 30 00:00:00 1899 ]

Napięcie u[Author ID1: at Sun Nov 8 12:27:00 1998 ]U[Author ID1: at Sun Nov 8 12:27:00 1998 ]_C(t) ma[Author ID1: at Sun Nov 8 12:28:00 1998 ]ma[Author ID1: at Sun Nov 8 12:28:00 1998 ] [Author ID1: at Sun Nov 8 12:27:00 1998 ] [Author ID1: at Sun Nov 8 12:27:00 1998 ]postać:

Dodatkowym parametrem tego obwodu jest stała czasowa :

[Author ID1: at Sun Nov 8 12:29:00 1998 ] [Author ID1: at Sun Nov 8 12:29:00 1998 ] [Author ID1: at Wed Nov 11 12:03:00 1998 ] [Author ID1: at Sun Nov 8 12:29:00 1998 ][Author ID0: at Thu Nov 30 00:00:00 1899 ]

 = RC[Author ID1: at Wed Nov 11 12:04:00 1998 ][Author ID1: at Wed Nov 11 12:04:00 1998 ][Author ID1: at Wed Nov 11 12:04:00 1998 ][Author ID1: at Wed Nov 11 12:04:00 1998 ][Author ID1: at Wed Nov 11 12:04:00 1998 ]
[Author ID1: at Wed Nov 11 12:04:00 1998 ]

która określa szybkość zmian [Author ID1: at Wed Nov 11 12:10:00 1998 ]prądu [Author ID1: at Wed Nov 11 12:06:00 1998 ][Author ID1: at Wed Nov 11 12:10:00 1998 ]n[Author ID1: at Wed Nov 11 12:10:00 1998 ]a[Author ID1: at Wed Nov 11 12:10:00 1998 ]p[Author ID1: at Wed Nov 11 12:10:00 1998 ]i[Author ID1: at Wed Nov 11 12:10:00 1998 ]ę[Author ID1: at Wed Nov 11 12:10:00 1998 ]c[Author ID1: at Wed Nov 11 12:10:00 1998 ]i[Author ID1: at Wed Nov 11 12:10:00 1998 ]a[Author ID1: at Wed Nov 11 12:10:00 1998 ] [Author ID1: at Wed Nov 11 12:10:00 1998 ]U[Author ID1: at Wed Nov 11 12:10:00 1998 ]i[Author ID1: at Sun Nov 8 12:29:00 1998 ][Author ID1: at Wed Nov 11 12:10:00 1998 ]_L[Author ID1: at Wed Nov 11 12:05:00 1998 ][Author ID1: at Wed Nov 11 12:10:00 1998 ]_C[Author ID1: at Wed Nov 11 12:10:00 1998 ]_p[Author ID1: at Wed Nov 11 12:10:00 1998 ].[Author ID1: at Wed Nov 11 12:10:00 1998 ] [Author ID1: at Wed Nov 11 12:10:00 1998 ][Author ID0: at Thu Nov 30 00:00:00 1899 ]

[Author ID0: at Thu Nov 30 00:00:00 1899 ]

DANE obwodu RC:

Obliczenia dla różnych wartości rezystancji:

1.) [Author ID1: at Wed Nov 11 12:10:00 1998 ][Author ID1: at Wed Nov 11 12:09:00 1998 ][Author ID0: at Thu Nov 30 00:00:00 1899 ]

E[Author ID1: at Wed Nov 11 12:09:00 1998 ] [Author ID1: at Wed Nov 11 12:09:00 1998 ]=[Author ID1: at Wed Nov 11 12:09:00 1998 ] [Author ID1: at Wed Nov 11 12:09:00 1998 ]1[Author ID1: at Wed Nov 11 12:09:00 1998 ]0[Author ID1: at Wed Nov 11 12:09:00 1998 ]V[Author ID1: at Wed Nov 11 12:09:00 1998 ] [Author ID1: at Wed Nov 11 12:09:00 1998 ]u[Author ID1: at Wed Nov 11 12:09:00 1998 ]([Author ID1: at Wed Nov 11 12:09:00 1998 ]0[Author ID1: at Wed Nov 11 12:09:00 1998 ]^-[Author ID1: at Wed Nov 11 12:09:00 1998 ])[Author ID1: at Wed Nov 11 12:09:00 1998 ]=[Author ID1: at Wed Nov 11 12:09:00 1998 ]0[Author ID1: at Wed Nov 11 12:09:00 1998 ]V[Author ID1: at Wed Nov 11 12:09:00 1998 ] [Author ID1: at Wed Nov 11 12:09:00 1998 ] [Author ID1: at Wed Nov 11 12:09:00 1998 ]C[Author ID1: at Wed Nov 11 12:09:00 1998 ] [Author ID1: at Wed Nov 11 12:09:00 1998 ]=[Author ID1: at Wed Nov 11 12:09:00 1998 ] [Author ID1: at Wed Nov 11 12:09:00 1998 ]1[Author ID1: at Wed Nov 11 12:09:00 1998 ]0[Author ID1: at Wed Nov 11 12:09:00 1998 ][Author ID1: at Wed Nov 11 12:09:00 1998 ]F[Author ID1: at Wed Nov 11 12:09:00 1998 ][Author ID0: at Thu Nov 30 00:00:00 1899 ]

R₁ = 901[Author ID1: at Wed Nov 11 12:09:00 1998 ]0 [[Author ID1: at Wed Nov 11 12:09:00 1998 ][Author ID1: at Wed Nov 11 12:09:00 1998 ]

2.) R₂ = 20005[Author ID1: at Wed Nov 11 12:09:00 1998 ] [[Author ID1: at Wed Nov 11 12:09:00 1998 ][Author ID1: at Wed Nov 11 12:09:00 1998 ]

3.) R₃ = 3002[Author ID1: at Wed Nov 11 12:11:00 1998 ]0 [[Author ID1: at Wed Nov 11 12:11:00 1998 ][Author ID1: at Wed Nov 11 12:11:00 1998 ]

-->Dane pozosta[Author ID1: at Wed Nov 11 12:11:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]-->łe: [Author ID1: at Wed Nov 11 12:11:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]-->E=[Author ID1: at Wed Nov 11 12:12:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]--> [Author ID1: at Wed Nov 11 12:12:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]-->10[Author ID1: at Wed Nov 11 12:12:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]--> [Author ID1: at Wed Nov 11 12:12:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]-->[V[Author ID1: at Wed Nov 11 12:12:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]-->][Author ID1: at Wed Nov 11 12:12:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]--> ; [Author ID1: at Wed Nov 11 12:13:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]-->L[Author ID1: at Wed Nov 11 12:13:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]-->=[Author ID1: at Wed Nov 11 12:13:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]-->0[Author ID1: at Wed Nov 11 12:13:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]-->.[Author ID1: at Wed Nov 11 12:13:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]-->15[Author ID1: at Wed Nov 11 12:13:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]--> [Author ID1: at Wed Nov 11 12:13:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]-->[[Author ID1: at Wed Nov 11 12:13:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]-->H[Author ID1: at Wed Nov 11 12:13:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]-->][Author ID1: at Wed Nov 11 12:13:00 1998 ][Author ID1: at Wed Nov 11 12:12:00 1998 ]-->[Author ID0: at Thu Nov 30 00:00:00 1899 ]

Wyniki:

R   ]	 ms]	I(t = 0) [ mA ]	UU = E = UC [ V ]
900	9	11.1	10
2000	20	5	10
3000	30	3.3	10

Obliczenia dla zmienionych warunków początkowych:

E = 10V u(0^-)=5V C = 10F

W tym przypadku stała całkowania A (dla chwili t = 0)wynosi:

R   ]	 ms]	I(t = 0) [ mA ]	UC(t = 0) [ V ]
2000	20	2	5

Wnioski:

Opis wpływu parametru C na układ:

Zamykając w chwili t = 0 wyłącznik, włączamy napięcie E do połączenia szeregowego elementów RC, wskutek czego kondensator ładuje się przez rezystor R. ( uC[Author ID1: at Sun Nov 8 12:37:00 1998 ](0-) = uC[Author ID1: at Sun Nov 8 12:37:00 1998 ](0+) )

Po upływie dostatecznie długiego czasu od chwili t = 0 kondensator naładuje się do napięcia E i wówczas prąd I w układzie będzie równy 0 ([Author ID1: at Sun Nov 8 12:37:00 1998 ]zero)[Author ID1: at Sun Nov 8 12:37:00 1998 ].

Opis wpływu parametru R na układ:

Zwiększając wartość rezystancji w obwodzie zwiększamy również stałą czasową . Gdy zwiększa się stała czasowa to zmniejsza się wartość prądu w obwodzie, a tym samym wydłuża się czas ustalenia wartości napięcia na kondensatorze.

Opis wpływu zmiany warunków początkowych napięcia :

Warunek początkowy u(0^-) = 5V powoduje skrócenie czasu ustalenia się napięcia na kondensatorze o czas t_x, który można obliczyć z poniższego wzoru:

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