Question

For an $LCR$ circuit, the power transferred from the driving source to the driven oscillator is $P=I^{2}Z\cos \varphi$.

• A. Here, the power factor $\cos \varphi \ge 0,P\ge 0$
• B. The driving force can give no energy to the oscillator $(P=0)$ in some cases
• C. The driving force cannot syphon Out $(P<0)$ the energy out of oscillator.
• D. All of these

Answer 1

Answer: (A), (B), (C)

Here, the power factor $\cos \varphi \ge 0,P\ge 0$
The driving force can give no energy to the oscillator $(P=0)$ in some cases
The driving force cannot syphon Out $(P<0)$ the energy out of oscillator.

Power Factor:

(1) It may be defined as cosine of the angle of lag or lead $(i.e,\cos \varphi )$

(2) It is also defined as the ratio of resistance and impedance $(i.e,\frac{R}{Z})$

(3) The ratio $=\frac{\text{True power}}{\text{Apparnet power}}=\frac{W}{VA}=\frac{kW}{kVA}=\cos \varphi$

In the given problem power transferred,

$P=I^{2}Z\cos \varphi$

where $I$ is the current, $Z=$ Impedance and $\cos \varphi$ is power factor

(a) As power factor, $\cos \varphi =\frac{R}{Z}$

where $R>0$ and $Z>0$

$\Rightarrow \cos \varphi >0\Rightarrow P>0$

(b) When $\varphi =\frac{\pi }{2}$ (in case of $L$ of $C$), $P=0$.

(c) From (a), it is clear that $P<0$ is not possible