(Solved): 4. The equations that respectively describe the time-varying voltage v(t), established across an in ...

4. The equations that respectively describe the time-varying voltage $\mathbf{v}(t)$, established across an inductor and time-varying current $i(t)$ flowing through an inductor in an RL circuit connected to a d.c. voltage source when a switch is thrown at time 0 are given by: $v(t)=V_{\mathbf{s}}{\mathrm{e}}^{-t/T}\text{ and }i(t)=I_{\mathbf{L}}\cdot \left(1-{\mathrm{e}}^{-/t}\right)$ where the throw of the switch activates the two behaviors at time 0 . The constant value $\tau$, as you may recall, describes the circuit's time constant. (Each part worth 3 points.) (a) In your exam booklet, write a Command Window sequence that defines the values of vS (MATLAB-ese for $V_{\mathrm{s}}$ ) to be 6 volts, tau to be $50\mu \sec$, and $I_{\text{s to }}$ to be $4\mathrm{mA}$. (b) Then, continue the coding sequence to define the vector, $t$ such that it spans a time sequence starting at 0 and ending at $6\tau$ (i.e., tau) where the time between adjacent elements represents $1\mu$ sec. (c) Use all the above to write the vectors $\mathbf{v}$ and $i$ to represent the respective equations $\mathbf{v}(t)$ and $\mathbf{i}(t)$ as given above. (d) Then use the vector pairs to make a plot of $v(t)$ and i(t) on the same time axis over the $6\tau$ time span where the time axis is expressed in $\mu$ sec, the voltage plot is expressed in volts, and the current plot is expressed in $\mathbf{mA}$. (e) Use the $t,v$, and $i$ vectors to write Command Window code that displays a formatted table showing values the instantaneous values for the voltages and currents every $10\mu \sec$ from 0 up through $2\tau$. The table should show the time values as integers where the times are expressed in $\mu \sec$, the voltages are expressed in volts, and the currents are expressed in $\mathrm{mA}$.