Final answer:
The voltage expression v(t)=5sin(10⁶ t) V for an inductor with an initial current i(0)=-0.5 A allows finding current i(t), power p(t), and the energy stored in the inductor. To plot these, one must solve for current by integrating the voltage, then find power by multiplying voltage and current, and calculate energy as LI²/2.
Step-by-step explanation:
The voltage across a 10-µH inductance given by v(t)=5sin(10⁶ t) V and the initial current i(0)=-0.5 A allows us to find expressions for the current, power, and stored energy for t>0. The expression for the current in the inductor can be found by integrating the voltage across the inductor with respect to time and considering the initial condition. Power at any time t is given by the product of the voltage across and the current through the inductor. The energy stored in the inductor is calculated as LI²/2, where L is the inductance and I is the current at time t.
To sketch the waveforms, one would plot v(t), i(t), and power p(t) as a function of time t on a graph, using a sinusoidal shape for voltage and current, and a power waveform that reflects the product of these two. Calculating and plotting these values requires solving differential equations and determining constants from initial conditions.