Question

In ac circuit with voltage \(\mathrm{V}\) and current \(\mathrm{I}\), the power dissipated is. (a) VI (b) \((1 / 2) \mathrm{VI}\) (c) \((1 / \sqrt{2}) \mathrm{VI}\) (d) Depends on the phase between \(\mathrm{V}\) and I

Short answer

The short answer is: (d) Depends on the phase between V and I, as the power in AC circuits is given by the formula \(P = VI \times \cos{\phi}\), where the power dissipated depends on the phase angle \(\phi\) between voltage and current.

Step-by-step solution

Power formula for AC circuits

The power in an AC circuit is given by the formula: \(P = VI \times \cos{\phi}\) Where P is the power dissipated, V is the voltage, I is the current, and \(\phi\) is the phase angle between the voltage and current waveforms.

Evaluate the given options

Now let's evaluate each option considering the power formula. (a) VI: This would be the power formula if there were no phase difference between voltage and current, i.e., \(\phi = 0\). However, in an AC circuit, the phase difference between voltage and current may not always be zero. (b) \((1 / 2) VI\): This is not related to the power formula in AC circuits, as it doesn't include the phase angle \(\phi\). (c) \((1 / \sqrt{2}) VI\): This is again not related to the power formula in AC circuits, as it doesn't include the phase angle \(\phi\). (d) Depends on the phase between V and I: This is the correct option, as the power in AC circuits is given by the formula \(P = VI \times \cos{\phi}\), where the power dissipated depends on the phase angle \(\phi\) between voltage and current. So, the correct option is (d) Depends on the phase between V and I.