Kadanda Konsansar

Idan lokacin da a sanya wani kumbin da ba a yi shiga ko kuma da shiga da yawa don hukuma mai tsarki da yawan shiga da shi (a cikin kumbin da ya shiga da yawa) ita ce zai samu shiga daga hukumar. Wannan zai haɗa shiga a kan kumbin tare da yanayi har zuwa lokacin da ta fi shiga da yawan hukumar.

A tabbata a sanya kumbin da shiga C a kan tashar da yanayi R. A tabbata a sanya wannan takamƙar kumbin da tashar da hukumar da yawan shiga V a kan takamƙar push switch S.
A fada ake iya ɗauka kumbin. Lokacin da a sauki takamƙar, saboda kumbin ba a yi shiga, ba a samu yawan shiga a kan kumbin, kuma kumbin zai ɗaya a kan maimaita. A lokacin haka shiga zai fara a gama a kan kumbin. Shiga a kan takamƙar zai kasance ne a kan yanayi R.

Saboda haka, shiga na farko shine V/R. Daga baya yawan shiga zai fara a gama a kan kumbin, kuma wannan yawan shiga ya faru a kan kumbin yana ciki a kan abin da ke hukumar. Saboda haka, shiga a kan takamƙar zai fara a rage. Lokacin da yawan shiga a kan kumbin yana ciki a kan abin da ke yawan shiga na hukumar, shiga zai kasance zero. Yawan shiga yana fara a gama a kan kumbin a lokacin da ake yi shiga. Za a duba a matsayin daraja da yawan shiga yake faru a kan kumbin shine dv/dt a kan lokacin t. Shiga a kan kumbin a lokacin haka shine

Amfani da, Kirchhoff’s Voltage Law, a kan takamƙar a lokacin haka, za a iya rubuta,

Integrating both side we get,

Now, at the time of switching on the circuit, voltage across the capacitor was zero. That means, v = 0 at t = 0.
Putting these values in above equation, we get

After getting the value of A, we can rewrite the above equation as,



Now, we know that,

This is the expression of charging current I, during process of charging.
The current and voltage of the capacitor during charging is shown below.

Here in the above figure, Io is the initial current of the capacitor when it was initially uncharged during switching on the circuit and Vo is the final voltage after the capacitor gets fully charged.
Putting t = RC in the expression of charging current (as derived above), we get,

So at the time t = RC, the value of charging current becomes 36.7% of initial charging current (V / R = Io) when the capacitor was fully uncharged. This time is known as the time constant of the capacitive circuit with capacitance value C farad along with the resistance R ohms in series with the capacitor. The value of voltage developed across that capacitor at the time constant is

Here Vo is the voltage finally developed across the capacitor after the capacitor is fully charged and it is same as source voltage (V = Vo).

Source: Electrical4u.

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