Question

The average power dissipated in $A.C.$ circuit is $2$ watt. If a current flowing through a circuit is $2A$ and impedance is $1\Omega$, what is the power factor of the AC circuit ?

• A. 0.5
• B. 1
• C. 0
• D. $\frac{1}{\sqrt{2}}$

Answer 1

Answer: (A)

As average power
$\bar{P}=2W,i_{rms}=2A$
Impedance $Z=1\Omega$
Power factor $(\cos \varphi )=?$
We know that
$\bar{P}=V_{rms}\times i_{rms}\cdot \cos \varphi$
$\bar{P}=i_{rms}^{2}Z\cdot \cos \varphi$
$\left(\because V_{rms}=i_{rms}\cdot Z\right)$
$\cos \varphi =\frac{\bar{P}}{i_{rms}^2\cdot Z}=\frac{2}{(2{)}^2\times 1}$
$=\frac{2}{4}=\frac{1}{2}=0.5$