Identify peak values and phase angles

From the given equations, the peak voltage $V_m = 10$ V and peak current $I_m = 10$ A · The phase angles are $\theta_v = -\pi/6$ and $\theta_i = \pi/6$.

$V_m = 10, I_m = 10, \theta_v = -30°, \theta_i = 30°$

Calculate the phase difference

The phase difference $\phi$ between voltage and current is given by $\phi = \theta_i - \theta_v$.

$\phi = 30°- (-30°) = 60°$

Calculate RMS values

The RMS values are derived from peak values as $V_{rms} = V_m/\sqrt{2}$ and $I_{rms} = I_m/\sqrt{2}$.

$V_{rms} = \frac{10}{\sqrt{2}}, I_{rms} = \frac{10}{\sqrt{2}}$

Calculate the power

Substitute the values into the average power formula $P = V_{rms} I_{rms} \cos(\phi)$, where $\cos(60°) = 0.5$.

$P = \frac{10}{\sqrt{2}} \times \frac{10}{\sqrt{2}} \times \cos(60°) = \frac{100}{2} \times 0.5 = 25 \text{ W}$