Question

An $\text{AC}$ source rated $100\text{V}\left(rms\right)$ supplies a current of $10\text{A}\left(rms\right)$ to a circuit. The average power delivered by the source

• A. must be $1000\text{W}$
• B. may be $1000\text{W}$
• C. may be greater than $1000\text{W}$
• D. may be less than $1000\text{W}$

Answer 1

Answer: (B), (D)

may be less than $1000\text{W}$

The average power delivered by the source is given by:

$P_{avg}=V_{rms}{I}_{rms}\cos \varphi$

Where $\cos \varphi$ is the power factor of the circuit.

Given, $V_{rms}=100\text{V}$ and $I_{rms}=10\text{A}$

$\Rightarrow P_{avg}=100\times 10\cos \varphi =1000\cos \varphi$

The value of $\cos \varphi$ lies between $[-1,1]$.

Therefore, power delivered by the source would be either equal to $1000\text{W}$ or less than $1000\text{W}$ depending on the elements connected in the circuit.

Hence, options $\left(B\right)$ and $\left(D\right)$ are the correct answers.

Why this question : This question tests the basic understanding of the power factor of a circuit.