(Solved): The spacecraft is nearly ready for takeoff! The last task is to attach the start capacitor to the s ...

The spacecraft is nearly ready for takeoff! The last task is to attach the start capacitor to the ship in a simple RC-circuit. Your computer warns you that some adjustments may need to be made if the heat generated in the resistor over the initial time interval is higher than a given threshold. Your computer is able to provide the following information, along with a note that the units are already accounted for in the equations: Heat Generated in Resistor over the first 2 seconds: $Q=\frac{V_b^2}{R}{?}_0^2{e}^{?2t/(RC)}dt$ joules Voltage of the Battery: ${\mathrm{V}}_{\mathrm{b}}=4$ volts Resistance: $\mathrm{R}=4$ ohms Capacitance: $C=\frac{1}{4}$ farads Maximum Heat Allowed in Resistor: ${\mathrm{Q}}_{\max }=2$ joules Is the heat generated in the resistor over the first 2 seconds below the maximum allowable threshold? Yes No What is the difference between the maximum threshold (provided above by your omputer) and the amount of heat generated in the resistor (that you calculated)? Provide a ositive value up to three decimal places. joules