An inductor $L=15H$ and a resistor $R=1000$ are connected in series with an AC power source providing voltage of $V=10sin(2ft)V,$ where $f=100kHz,$ as shown in the figure on the next page. The current I in the circuit is determined from the solution of the equation:

$\frac{dI}{dt}=\frac{10sin(2ft)}{L}-\frac{R}{L}I$

Solve the equation and plot the current as a function of time for $0t{10}^{-4}s$ with $I(0)=0.$ Solve the problem using your $4$th$-$order Runge$-$Kutta Function. Use a time step of $1{10}^{-9}s.($Note that the ODE depends on the current and time, and be careful with units in the sin function.$)$

Figure $3$: DC inductor$-$resistor circuit

Figure $4$: AC inductor$-$resistor circuit