An LCR circuit contains resistance of 110 $\Omega$ and a supply of 220 V at 300 rad/s angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by 45°. If on the other hand, only inductor is removed the current leads by 45° with the applied voltage. The rms current flowing in the circuit will be

Correct Option - 2


Detailed Solution:

When capacitor is removed

tan 45° = $\frac{X_L}{X_R}\Rightarrow \omega L=R$

When inductor is removed.

$tan45°=\frac{X_C}{X_R}\Rightarrow \frac{1}{\omega C}=R$

$i_0=\frac{V_0}{Z}=\frac{V_0}{\sqrt[]{R^2+{\left(\omega L-\frac{1}{\omega C}\right)}^2}}=\frac{V_0}{R}=\frac{220}{110}=2A$

<p>When capacitor is removed</p><p>tan 45° =&nbsp;<math><mrow><mfrac><mrow><msub><mrow><mi>X</mi></mrow><mrow><mi>L</mi></mrow></msub></mrow><mrow><msub><mrow><mi>X</mi></mrow><mrow><mi>R</mi></mrow></msub></mrow></mfrac><mo>⇒</mo><mi>ω</mi><mi>L</mi><mo>=</mo><mi>R</mi></mrow></math></p><p>When inductor is removed.</p><p><math><mrow><mi>t</mi><mi>a</mi><mi>n</mi><mn>4</mn><mn>5</mn><mo>°</mo><mo>=</mo><mfrac><mrow><msub><mrow><mi>X</mi></mrow><mrow><mi>C</mi></mrow></msub></mrow><mrow><msub><mrow><mi>X</mi></mrow><mrow><mi>R</mi></mrow></msub></mrow></mfrac><mo>⇒</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>ω</mi><mi>C</mi></mrow></mfrac><mo>=</mo><mi>R</mi></mrow></math></p><p><math><mrow><msub><mrow><mi>i</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mrow><mi>Z</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mrow><mroot><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mrow><mo> (</mo><mrow><mi>ω</mi><mi>L</mi><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>ω</mi><mi>C</mi></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow></mrow></mroot></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mrow><mi>R</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mn>2</mn><mn>0</mn></mrow><mrow><mn>1</mn><mn>1</mn><mn>0</mn></mrow></mfrac><mo>=</mo><mn>2</mn><mi>A</mi></mrow></math></p><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1755056522phpwyxqZQ.jpeg" alt="" width="115" height="214" loading="lazy"></picture></div></div>

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