Concept:Average real power in an AC circuit depends on the cosine of the phase angle difference \(\phi\) between voltage and current.
Formula / Reaction:$$P = V_{\text{rms}} I_{\text{rms}} \cos\phi$$
Solution:- Using \(\cos(\omega t) = \sin\left(\omega t + \frac{\pi}{2}\right)\), the voltage equation becomes \(V = 5 \sin\left(\omega t + \frac{\pi}{2}\right)\).
- Current is \(i = 2 \sin(\omega t)\).
- The phase difference is \(\phi = 90^\circ\) (\(\pi/2\text{ rad}\)).
- \(P = V_{\text{rms}} I_{\text{rms}} \cos(90^\circ) = 0\text{ W}\).
Why other options are incorrect:- Opt_B: \(10\text{ W}\) is the product of peak values \(V_0 I_0\) assuming \(\cos\phi = 1\).
- Opt_C: \(5\text{ W}\) is \(\frac{1}{2} V_0 I_0\), valid only for in-phase waveforms.
- Opt_D: \(2.5\text{ W}\) is an incorrect fraction.
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