Final answer:
The instantaneous power in an AC circuit with a sinusoidal voltage and current can be calculated by multiplying the voltage and current equations, taking into account any phase differences. The resulting power equation would then be plotted over the specified time to visualize the power waveform.
Step-by-step explanation:
The student has asked to plot the instantaneous power of an AC circuit with a sinusoidal voltage source v(t) = 15.25 sin(377t) and a sinusoidal current source i(t) = 11.33 sin(377t - 30°) for 0.1 seconds. The instantaneous power p(t) in an AC circuit is the product of the instantaneous voltage and current, so it can be written as p(t) = v(t) × i(t).
To find the instantaneous power, we must account for the phase difference between the voltage and the current. We first need to convert the phase difference of 30° to radians, which is π/6. Thus, the current equation will be i(t) = 11.33 sin(377t - π/6).
The next step would be to multiply the voltage and current equations. Since this calculation involves trigonometric functions with a phase shift, we would typically use trigonometric identities to find a function for p(t) that can be easily plotted. However, in this case, it's simpler to do point-by-point multiplication using software that can plot the resulting wave over the specified time period of 0.1 seconds.