Question

Real power consumption in a circuit is least when it contains.
(A) High $R$,low$L$
(B) High $R$,high$L$
(C) low$R$, high$L$
(D) high$L$,low $C$

Answer 1

Hint: Power factor(PF) is the ratio of working power, measured in kilowatts(kW) to apparent power, measure in kilovolt amperes (kVA). PF expresses the ratio of true power delivered to the circuit. A 96% power factor demonstrates more efficiency than 75% power factor.

Complete step by step answer:
Average power consumption in a $R - L$circuit given by,
$\bar P{V_{rms}}{i_{rms}}\cos \phi $
And power factor,
$\cos \phi = \dfrac{R}{{\sqrt {{R^2} + {\omega ^2}{L^2}} }}$
$\bar P$will be minimum when $\cos \phi $is minimum.
For low $R$(nearly zero) and high $L$,
$\cos \phi = 0$(approx.)
Hence, $\bar P = 0$
Therefore power consumption in a $R - L$circuit is least, when it contains low $R$,high $L$.
Average power consumption in a
$R - C$circuit given by,
$\bar P{V_{rms}}{i_{rms}}\cos \phi $ . . . (1)
And power factor,
$\cos \phi = \dfrac{R}{{\sqrt {{R^2} + 1/{\omega ^2}{C^2}} }}$. . . (2)
$\bar P$will be minimum when
$\cos \phi $ is not minimum.
For high $R$and low $C$, $\cos \phi $is not minim from above equation (2)
Hence,$\bar P \ne 0$
Therefore, power consumption in a $R - C$circuit is not least, when it contains high $R$,low $C$.

So, the correct answer is “Option C”.

Note:
The power factor is the relationship of current and voltage in AC electrical distribution systems. Under ideal conditions current and voltage are ‘in phase’ and the power factor is “100%” if inductive loads are present, power factor less than 100%. The power factor can get values in the range from 0 to 1. When all the power is reactive power with no real power. The power is 0. When all power is real power with no reactive power- the power factor is 1.