A series \(LCR\) circuit is connected to an \(AC\) source of \(220\,V , 50\,Hz\). The circuit contains a resistance \(R =80\,\Omega\), an inductor of inductive reactance \(X _{ L }=70\,\Omega\), and a capacitor of capacitive reactance \(X _{ C }=130\,\Omega\). The power factor of circuit is \(\frac{ X }{10}\). The value of \(x\) is:

Explanation:
1. Calculation of Impedance (Z):
The total impedance of a series LCR circuit is determined by the formula:
\( Z = \sqrt{R^2 + (X_C - X_L)^2} \)
Substituting the given values into the equation:
\( Z = \sqrt{80^2 + (130 - 70)^2} = \sqrt{80^2 + 60^2} = \sqrt{6400 + 3600} = 100\ \Omega \)

2. Calculation of Power Factor (\( \cos\phi \)):
The power factor of an alternating current circuit is given by:
\( \cos\phi = \frac{R}{Z} = \frac{80}{100} = 0.8 \)

3. Finding the value of x:
The question defines the power factor as the fraction \( \frac{x}{10} \). Equating the calculated value to this format gives:
\( \frac{x}{10} = 0.8 \implies \frac{x}{10} = \frac{8}{10} \implies x = 8 \)

Hence, Option B is the correct choice.