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

For resonance frequency ω L = 1 ω C ⇒ ω = 1 L C = 1 10 × 10 - 3 × 1 × 10 - 6 = 1 10 - 8 = 10 4 r a d / s e c f = ω 2 π = 10 4 2 π = 1.59 k H z

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Physics Class 12th Physics Alternating Current

In a series LCR circuit, the inductance L is 10mH, 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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Answered by

Raj Pandey | Contributor-Level 9

3 weeks ago

Correct Option - 1

Detailed Solution:

For resonance frequency

$\begin{array}{r} ω L = \frac{1}{ω C} \\ \Rightarrow ω = \frac{1}{\sqrt[]{L C}} = \frac{1}{\sqrt[]{10 \times 10^{- 3} \times 1 \times 10^{- 6}}} \\ = \frac{1}{\sqrt[]{10^{- 8}}} = 10^{4} r a d / s e c \\ f = (\frac{ω}{2 π}) = \frac{10^{4}}{2 π} = 1.59 k H z \end{array}$

For resonance frequency <math> <mtable columnalign="right"> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi>ω</mi> <mi mathvariant="normal">L</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mi>ω</mi> <mi mathvariant="normal">C</mi> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi> </mi> <mo>⇒</mo> <mi>ω</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mroot> <mrow> <mrow> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">C</mi> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>10</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </mrow> </msup> <mo>×</mo> <mn>1</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi> </mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mroot> <mrow> <mrow> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>8</mn> </mrow> </mrow> </msup> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> </mfrac> <mo>=</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> </mrow> </mrow> </msup> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">c</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi mathvariant="normal">f</mi> <mo>=</mo> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi>ω</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> <mo>=</mo> <mfrac> <mrow> <mrow> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>1.59</mn> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">H</mi> <mi mathvariant="normal">z</mi> </mrow> </mtd> </mtr> </mtable> </math>

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