An inductor of 0.5 mH, a capacitor of 200 $\mu F$  and a resistor of 2 $\Omega$  are connected in series with a 220V ac source. If the current is in phase with the emf, the frequency of ac source will be__________ × 10² Hz.

<p>Since current is in phase with voltage, it means circuit is in resonance, so we can write</p><p>f =&nbsp;<math><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>π</mi><mroot><mrow><mi>L</mi><mi>C</mi></mrow><mrow></mrow></mroot></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>π</mi><mroot><mrow><mrow><mo> (</mo><mrow><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow><mo>)</mo></mrow><mo>×</mo><mrow><mo> (</mo><mrow><mn>2</mn><mn>0</mn><mn>0</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow><mo>)</mo></mrow></mrow><mrow></mrow></mroot></mrow></mfrac></mrow></math></p><p><math><mrow><mo>⇒</mo><mi>f</mi><mo>=</mo><mfrac><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>4</mn></mrow></msup></mrow><mrow><mn>2</mn><mi>π</mi><mroot><mrow><mn>1</mn><mn>0</mn></mrow><mrow></mrow></mroot></mrow></mfrac><mo>≈</mo><mn>5</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msup><mi>H</mi><mi>z</mi></mrow></math>&nbsp;<math><mrow><mrow><mo> [</mo><mrow><mi>T</mi><mi>a</mi><mi>k</mi><mi>i</mi><mi>n</mi><mi>g</mi><mtext> </mtext><mtext> </mtext><mi>π</mi><mo>=</mo><mroot><mrow><mn>1</mn><mn>0</mn></mrow><mrow></mrow></mroot></mrow><mo>]</mo></mrow></mrow></math></p>

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