An LCR circuit contains resistance of

Question:

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

  1. $1 \mathrm{~A}$

  2.  $2.5 \mathrm{~A}$

  3. $1.5 \mathrm{~A}$

  4. $2 \mathrm{~A}$


Correct Option: , 4

Solution:

$\tan 45^{\circ}=\frac{1}{\omega C R}=\frac{\omega L}{R} \Rightarrow X_{L}=X_{C}$

$\Rightarrow$ resonance

$i=\frac{V}{R}$

$=\frac{220}{110}=2 \mathrm{~A}$

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