Question

In an a.c. circuit with phase voltage V and current I, the power dissipated is

• A. V.I
• B. depends on phase angle between V and I
• C. $\frac{1}{2}\times V.I$
• D. $\frac{1}{\sqrt2}\times V.I$

Answer 1

The Correct Option is B

To solve this question, we need to understand the concept of power dissipation in an AC circuit. In an AC circuit, the power dissipated (also known as the real power or active power) is given by the formula:

P = V \cdot I \cdot \cos(\phi)

Where:

• V is the RMS (Root Mean Square) voltage.
• I is the RMS current.
• \phi is the phase angle between the voltage and current.
• \cos(\phi) is the power factor of the circuit.

The phase angle \phi influences how effectively the current transfers energy from the source to the load. The term \cos(\phi) adjusts for the difference in time (or phase) between the voltage and the current waveforms. When the phase angle is 0 (purely resistive load), the power factor is 1, resulting in maximum power dissipation. However, for other values of phase angle, the power factor adjusts the real power dissipated in the circuit. Therefore, real power dissipated in an AC circuit depends on the phase angle between the voltage and current.

Let's analyze the provided options:

• Option 1: V \cdot I - This expression represents the apparent power, not the real power dissipated in the circuit. Hence, this option is incorrect.
• Option 2: Depends on phase angle between V and I - This is correct as explained above since the real power dissipated has a dependency on the phase angle through the \cos(\phi) factor.
• Option 3: \frac{1}{2} \times V \cdot I - This is not a standard formula for calculating real power or any component of AC power. This expression is incorrect in the context of AC power calculations.
• Option 4: \frac{1}{\sqrt{2}} \times V \cdot I - This expression might suggest half of the apparent power adjusted by a factor, but this is not the correct relation for calculating real power in AC circuits. Hence, this option is incorrect.

Thus, the correct answer is that the power dissipated in an AC circuit depends on the phase angle between V and I.