Question

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

• A. \(8\)
• B. \(6\)
• C. \(4\)
• D. \(7\)

Hint:

Z = sqrt(R^2 + (XL - XC)^2); power factor = R / Z.

Answer 1

The Correct Option is A

Step 1: Use the 3-4-5 pattern:
Resistance 80 and net reactance 60 form a right triangle with ratio 4:3. The hypotenuse is 100.

Step 2: Cosine:
$\cos\phi=\dfrac{\text{adjacent}}{\text{hypotenuse}}=\dfrac{80}{100}=0.8$.

Step 3: x:
$0.8=\dfrac x{10}$ gives $x=8$. Option (A).

Final Answer:
The 80, 60, 100 triangle gives cos phi = 0.8. \[ \boxed{A} \]