In a series LCR circuit, the inductance <math> <mi>L</mi> </math> is <math> <mn>10</mn> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">H</mi> </math> , capacitance <math> <mi mathvariant="normal">C</mi> </math> is <math> <mn>1</mn> <mi>μ</mi> <mi mathvariant="normal">F</mi> </math> and resistance <math> <mi mathvariant="normal">R</mi> </math> is <math> <mn>100</mn> <mi mathvariant="normal">Ω</mi> </math> . The frequency at which resonance

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

In a series LCR circuit, the inductance <math> <mi>L</mi> </math> is <math> <mn>10</mn> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">H</mi> </math> , capacitance <math> <mi mathvariant="normal">C</mi> </math> is <math> <mn>1</mn> <mi>μ</mi> <mi mathvariant="normal">F</mi> </math> &nbsp;and resistance <math> <mi mathvariant="normal">R</mi> </math> is <math> <mn>100</mn> <mi mathvariant="normal">Ω</mi> </math> . The frequency at which resonance

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Electron Drift Velocity Physics Alternating Current Physics Class 12th

In a series LCR circuit, the inductance $L$ is $10 m H$ , capacitance $C$ is $1 μ F$ and resistance $R$ is $100 Ω$ . The frequency at which resonance

Option 1 -

$1.59 k H z$

Option 2 -

$15.9 r a d / s$

Option 3 -

$15.9 k H z$

Option 4 -

$1.59 r a d / s$

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month 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>X</mi> </mrow> </mrow> <mrow> <mrow> <mi>c</mi> </mrow> </mrow> </msub> </math> is inversely proportional to <math> <mi>ω</mi> </math> the value of <math> <msub> <mrow> <mrow> <mi>X</mi> </mrow> </mrow> <mrow> <mrow> <mi>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 mathvariant="normal">X</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </math>  increases, therefore displacement current Id decreases. <!- [if !supportLineBreakNewLine]-> <!- [endif]->

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In a series LCR circuit, the inductance $L$ is $10 m H$ , capacitance $C$ is $1 μ F$ and resistance $R$ is $100 Ω$ . The frequency at which resonance

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In a series LCR circuit, the inductance L is 10 m H , capacitance C is 1 μ F and resistance R is 100 Ω . The frequency at which resonance

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In a series LCR circuit, the inductance $L$ is $10 m H$ , capacitance $C$ is $1 μ F$ and resistance $R$ is $100 Ω$ . The frequency at which resonance