Question

When an inductor and a resistor are connected in series to an AC source, the power factor of the circuit is \[ \frac{2}{\sqrt{13}}. \] If the same resistor and a capacitor are connected in series to the same AC source, then the power factor of the circuit is \[ \frac{1}{\sqrt2}. \] If these inductor, capacitor and resistor are connected in series to the same AC source, then the ratio of the resistance and impedance of the LCR circuit is

• A. \(1:\sqrt7\)
• B. \(2:\sqrt5\)
• C. \(2:\sqrt7\)
• D. \(1:\sqrt5\)

Hint:

For AC circuits, \[ \boxed{ \cos\phi=\frac{R}{Z}. } \] Also, \[ \boxed{ Z_{RL}=\sqrt{R^2+X_L^2},\qquad Z_{RC}=\sqrt{R^2+X_C^2}, } \] and for a series LCR circuit, \[ \boxed{ Z=\sqrt{R^2+(X_L-X_C)^2}. } \]

Answer 1

The Correct Option is B