An ac source is connected to a capacitor C. Due to decrease in its operating frequency:

Option 1 -

capacitive reactance remains constant

Option 2 -

capacitive reactance decreases.

Option 3 -

displacement current increases.

Option 4 -

displacement current decreases.

3 Views | Posted 3 weeks ago

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1 Answer

Answered by

Raj Pandey | Contributor-Level 9

3 weeks ago

Correct Option - 4

Detailed Solution:

Capacitive reactance $= \frac{1}{ω C} = X_{c}$ (say) on decreasing the operating frequency $ω$ reduces

As $X_{c}$ is inversely proportional to $ω$ the value of $X_{c}$ increase

$∴ I_{C} = I_{D}$

$= \frac{V_{o}}{X_{c}}$

As $X_{c}$ increases, therefore displacement current Id decreases.

Capacitive reactance <math> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mi>ω</mi> <mi mathvariant="normal">C</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <msub> <mrow> <mrow> <mi mathvariant="normal">X</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </math> (say) on decreasing the operating frequency <math> <mi>ω</mi> </math>  reducesAs <math> <msub> <mrow> <mrow> <mi mathvariant="normal">X</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </math> is inversely proportional to <math> <mi>ω</mi> </math>  the value of <math> <msub> <mrow> <mrow> <mi mathvariant="normal">X</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </math>  increase <math> <mo>∴</mo> <msub> <mrow> <mrow> <mi mathvariant="normal">I</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">C</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mrow> <mi mathvariant="normal">I</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">D</mi> </mrow> </mrow> </msub> </math> <!- [endif]-><!- [endif]-> <math> <mo>=</mo> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">V</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">o</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">X</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </math> <!- [endif]-><!- [endif]->As <math> <msub> <mrow> <mrow> <mi>X</mi> </mrow> </mrow> <mrow> <mrow> <mi>c</mi> </mrow> </mrow> </msub> </math>  increases, therefore displacement current Id decreases. <!- [if !supportLineBreakNewLine]-> <!- [endif]->

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