In AC circuit with source voltage e = 20 sin 1000 t is connected to series L – R circuit whose power factor is $\frac{1}{\sqrt[]{2}}$ . If E = 25 sin 2000 t, the new power factor is

Correct Option - 2


Detailed Solution:

Lω = 1000 L                            Lω = R.

New

R = 1000 L

2000 L

$cos\theta =\frac{R}{Z}$

$=\frac{1000L}{\sqrt[]{{\left(1000L\right)}^2+{\left(2000\text{?}L\right)}^2}}$

$=\frac{1}{\sqrt[]{1+4}}=\frac{1}{\sqrt[]{5}}$

 

<div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1758869886phpXSb3ij.jpeg" alt="" width="292" height="199" loading="lazy"></picture></div></div><p><span lang="EN-IN">L</span><span lang="EN-IN">ω</span><span lang="EN-IN"> = 1000 L&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span lang="EN-IN">&nbsp;L</span><span lang="EN-IN">ω</span><span lang="EN-IN"> = R.</span></p><p><u><span lang="EN-IN">New</span></u></p><p>R = 1000 L</p><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1758869927phpr7ipCR.jpeg" alt="" width="223" height="162" loading="lazy"></picture></div><div><p><span lang="EN-IN">2000 L</span></p><p><span contenteditable="false"> <math> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>θ</mi> <mo>=</mo> <mfrac> <mrow> <mi>R</mi> </mrow> <mrow> <mi>Z</mi> </mrow> </mfrac> </mrow> </math> </span></p><p><span contenteditable="false"> <math> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mn>0</mn> <mn>0</mn> <mn>0</mn> <mtext> </mtext> <mi>L</mi> </mrow> <mrow> <mroot> <mrow> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <mn>1</mn> <mn>0</mn> <mn>0</mn> <mn>0</mn> <mtext> </mtext> <mi>L</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <mn>2</mn> <mn>0</mn> <mn>0</mn> <mn>0</mn> <mtext>? </mtext> <mtext> </mtext> <mi>L</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> </mrow> </math> </span></p><p><span contenteditable="false"> <math> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mroot> <mrow> <mn>1</mn> <mo>+</mo> <mn>4</mn> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mroot> <mrow> <mn>5</mn> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> </mrow> </math> </span></p></div></div><p>&nbsp;</p>

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