Question

The power loss (\( P \)) in a dielectric is given by _________ where \( V \) is voltage, \( I \) is current, \( \delta \) is loss tangent

• A. \( P = VI \cos\delta \)
• B. \( P = \frac{V}{I} \cos\delta \)
• C. \( P = VI \sin\delta \)
• D. \( P = \frac{V}{I} \sin\delta \)

Hint:

The power loss in a dielectric is proportional to \( \sin\delta \), where \( \delta \) represents the loss tangent, measuring how much energy is dissipated in the material.

Answer 1

The Correct Option is C

The power loss in a dielectric material occurs due to dielectric dissipation and is determined using the following relation: \[ P = VI \sin\delta \] where: - \( V \) is the applied voltage, - \( I \) is the current, - \( \delta \) is the dielectric loss angle (also called the loss tangent).
Step 1: Understanding Dielectric Loss - The total power in an AC circuit is given by \( P = VI \cos\phi \), where \( \phi \) is the phase angle. - In a perfect capacitor, the phase angle between voltage and current is 90°, leading to no real power loss. - However, in real dielectrics, losses occur due to the imperfect insulation properties, represented by the loss tangent \( \tan\delta \). - The actual power loss is given by: \[ P = VI \sin\delta \]


Step 2: Evaluating the Options - Option (A) - Incorrect: Power loss is associated with \( \sin\delta \), not \( \cos\delta \).
- Option (B) - Incorrect: The formula uses \( VI \), not \( V/I \).
- Option (C) - Correct: \( P = VI \sin\delta \) correctly describes dielectric power loss.
- Option (D) - Incorrect: \( V/I \) does not correspond to the correct power loss equation.


Step 3: Conclusion Since the correct formula for dielectric power loss is \( P = VI \sin\delta \), the correct answer is option (C).