Question

An AC source of \(220\,V\) and \(50\,Hz\) is connected to an RLC circuit having resistance \(10\,\Omega\). The power factor is \(0.5\). Find the average power consumed.

• A. \(605\,W\)
• B. \(2420\,W\)
• C. \(1210\,W\)
• D. \(2200\,W\)

Hint:

Average power in AC circuits is \[ P=VI\cos\phi. \] Only the active component of current contributes to power consumption.

Answer 1

The Correct Option is B

Concept: The average power consumed in an AC circuit is \[ P=VI\cos\phi \] where \(\cos\phi\) is the power factor. Current is obtained using \[ I=\frac{V}{R}. \]

Step 1: Calculate current. Given, \[ V=220\,V \] \[ R=10\,\Omega \] Hence, \[ I=\frac{220}{10} \] \[ I=22\,A \]

Step 2: Calculate average power. Power factor, \[ \cos\phi=0.5 \] Therefore, \[ P=VI\cos\phi \] \[ =(220)(22)(0.5) \] \[ =2420\,W \]

Step 3: Compare with the options. The calculated value is \[ 2420\,W \] Thus the correct answer is \[ \boxed{(B)} \]