Question

The ratio of the apparent power to the average power in an AC circuit is equal to:
$
  A.\cos \theta \\
  B.\dfrac{1}{{\cos \theta }} \\
  C.{\text{Form Factor}} \\
  D.\dfrac{1}{{{{\cos }^2}\theta }} \\
 $

Answer 1

Hint: There are basically three powers involved in an AC circuit, namely, active power, reactive power, and true power. In this question, we need to determine the ratio of the apparent power to the average power in an AC circuit by using the general formulae of the same.

Complete step by step answer:
The product of the root mean square value of the voltage and the current flowing in the circuit is known as the apparent power in an AC circuit. It is denoted by the letter ‘S’ and is measured in Volt-Amperes (VA). Mathematically, $S = {V_{rms}}{I_{rms}} - - - - (i)$

The product of the root mean square value of the voltage and current flowing in the circuit with the cosine of the power angle is known as the Average power in the AC circuit. It is also known as the real power or the true power or the active power in the AC circuit. It is denoted by the letter ‘P’ and is measured in Watts (W). Mathematically, $P = {V_{rms}}{I_{rms}}\cos \theta - - - - (ii)$ where, $\theta $ is the power angle of the AC circuit.

  From equation (i) and (ii), we get:

$
  \dfrac{S}{P} = \dfrac{{{V_{rms}}{I_{rms}}}}{{{V_{rms}}{I_{rms}}\cos \theta }} \\
   = \dfrac{1}{{\cos \theta }} \\
 $

Hence, the ratio of the apparent power to the average power in an AC circuit is equal to $\dfrac{1}{{\cos \theta }}$.

So, the correct answer is “Option B”.

Note:
Students should be aware while using the different terms in the AC circuit. Here, true power, active power, and the average power all are the same. Here we can also say that the true power (or the average power) is the actual power consumed by the elements established in the AC circuit. When the reactive power component is eliminated from the apparent power, then, it is known to be the Active power or the Average power of the AC circuit.