A resistor of resistance $R$, inductor of inductive reactance $2 R$ and a capacitor of capacitive reactance…

A resistor of resistance $R$, inductor of inductive reactance $2 R$ and a capacitor of capacitive reactance $X_C$ are connected in series to an a.c. source. If the series LCR circuit is in resonance, then the power factor of the circuit and the value $\mathrm{X}_{\mathrm{C}}$ are respectively
  1. 0.5 and 4R
  2. 1 and 2 R
  3. 0.5 and 2R
  4. I and 4R

Solution

In LCR series circuit, at resonance, $\mathrm{X}_{\mathrm{C}}=\mathrm{X}_{\mathrm{L}}=2 \mathrm{R}$
Power factor, $\cos \phi=\frac{R}{Z}=\frac{R}{R}=1$

Asked in: AP EAMCET 2024 (21 May Shift 2)

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