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Electrostatic Potential And Capacitance

Question
CBSEENPH12039952
Wired Faculty App

A series R -C circuit is connected to an alternating voltage source. Consider tow situations:

1. When the capacitor is air filled.
2. When the capacitor is mica filled.

Current through resistor is i and voltage across capacitor is V then

  • Va < Vb

  • Va > Vb

  • ia >ib

  • Va = Vb

Solution

B.

Va > Vb

Net reactive capacitance,

in straight V space equals space straight V subscript straight o space sin space space ωt straight X subscript straight C space equals space fraction numerator 1 over denominator 2 πfC end fraction so comma space current space in space circuit comma space straight I space space equals space straight V over straight Z space equals space fraction numerator straight V over denominator square root of straight R squared plus open parentheses begin display style fraction numerator 1 over denominator 2 πfC end fraction end style close parentheses squared end root end fraction rightwards double arrow space straight I space equals space fraction numerator 2 πfC over denominator square root of 4 straight pi squared straight f squared straight C squared straight R squared space plus 1 end root end fraction space straight x space straight V Voltage space drop space across space capacitor comma space straight V subscript straight c space equals space straight I space straight x space space straight X subscript straight c equals space fraction numerator 2 πfC over denominator square root of 4 straight pi squared straight f squared straight C squared straight R space plus 1 end root end fraction space straight x space fraction numerator 1 over denominator 2 πfC end fraction straight i. straight e. comma space straight V subscript straight c space equals space fraction numerator straight V over denominator square root of 4 straight pi squared straight f squared straight C squared straight R squared plus 1 end root end fraction
when mica is introduced capacitance will increase hence, voltage across capacitor get decrease.

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