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$33$ seconds:$$Q$=$V$2$bR$30$e$2$t$/($RC$)$dtQ$=$Vb$2$R$03$e$2$t$/($RC$)$dt$$joules

Voltage of the Battery:$$Vb$=2$Vb$=2$volts

Resistance:$$R$=2$R$=2$ohms

Capacitance:$$C$=12$C$=12$farads

Maximum Heat Allowed in Resistor:$$Qmax$=1$Qmax$=1$joules

$$

Is the heat generated in the resistor over the first $3$seconds$$below the maximum allowable threshold?

Yes

No

What is the difference between the maximum threshold $($provided above by your computer$)$and the amount of heat generated in the resistor $($that you calculated$)?$ Provide a positive value up to three decimal places.

$$joules