Question

An AC circuit has \(V_{\mathrm{rms}}=230\,\mathrm{V}\), \(I_{\mathrm{rms}}=5\,\mathrm{A}\) and power factor \(=0.8\), then the active power consumed is

• A. \(460\,\mathrm{W}\)
• B. \(575\,\mathrm{W}\)
• C. \(920\,\mathrm{W}\)
• D. \(1150\,\mathrm{W}\)

Hint:

The active (real) power in an AC circuit is \[ \boxed{ P=VI\cos\phi } \] where \(\cos\phi\) is the power factor.

Answer 1

The Correct Option is C

Step 1: Use the active power formula. For an AC circuit, \[ P=V_{\mathrm{rms}}I_{\mathrm{rms}}\cos\phi. \] Given, \[ V_{\mathrm{rms}}=230\,\mathrm{V},\qquad I_{\mathrm{rms}}=5\,\mathrm{A},\qquad \cos\phi=0.8. \]

Step 2: Substitute the values. \[ P = 230\times5\times0.8 = 920\,\mathrm{W}. \] Hence, \[ \boxed{920\,\mathrm{W}} \] Therefore, \[ \boxed{(C)} \] is the correct answer.