Question

The average power dissipated in $A.C.$ circuit is $2$ watt. If a current flowing through a circuit is $2\, A$ 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
$\bar{P}=2 W , i_{ rms }=2 A$
Impedance $Z=1\, \Omega$
Power factor $(\cos \phi)=?$
We know that
$\bar{P} =V_{ rms } \times i_{ rms } \cdot \cos \phi$
$\bar{P} =i_{ rms }^{2} Z \cdot \cos \phi$
$\left(\because V_{ rms }=i_{ rms } \cdot Z\right)$
$\cos \phi =\frac{\bar{P}}{i_{ rms }^{2} \cdot Z}=\frac{2}{(2)^{2} \times 1}$
$=\frac{2}{4}=\frac{1}{2}=0.5$