Question

In an ac circuit with voltage $V$ and current $I$, the power dissipated is.

• A. $VI$
• B. $\frac{VI}{2}$
• C. $\frac{VI}{\sqrt{2}}$
• D. Depends on the phase between $V$ and $I$

Answer 1

The correct option is D

Depends on the phase between $V$ and $I$

Correct Option: Option D

1. Power dissipation: The heat generated in the circuit as a derivative of its primary action is power dissipation.
2. In an AC circuit, there will be a phase difference between current and voltage.
3. The formula for the power dissipated in an AC circuit is $P=VI\cos \theta$ where $\theta$is the phase difference between $V$ and $I$.
4. So, the power dissipated in an AC circuit depends on the phase between $V$ and $I$. So, this option is correct for constant $V$ and $I$.

Incorrect Options:

Option A

The formula for the power dissipated in an AC circuit is $P=VI\cos \theta$. It is not a constant value, since the phase difference changes. Its value will be equal to $VI$ only when $\cos \theta =1$. So, this option is incorrect.

Option B

The formula for the power dissipated in an AC circuit is $P=VI\cos \theta$. It is not a constant value, since the phase difference changes. Its value will be equal to $\frac{VI}{2}$ only when $\cos \theta =\frac{1}{2}$. So, this option is incorrect.

Option C

The formula for the power dissipated in an AC circuit is $P=VI\cos \theta$. It is not a constant value, since the phase difference changes. Its value will be equal to $\frac{VI}{\sqrt{2}}$ only when $\cos \theta =\frac{1}{\sqrt{2}}$. So, this option is incorrect.

Hence, the answer is option D.