$1.$

Derive the Capacitor Voltage $($Vc$)$ charging equation $($express in terms of VF and $,$ where $VF$ is the final steady$-$state voltage and $$ is the time constant$).$

$2.$

What is the value of VF in the equation from question $(1)?$

$3.$

What is the value of $t$ in the equation from question $(1)?($Unit: $s)$

$4.$

What is the value of Vc $($capacitor voltage$)$ at $10s$ after the switch is closed? $($Unit: V$)$

$5.$

After the capacitor is fully charged, the switch is first opened. Then the voltage source is disconnected and the original terminals of the capacitor are connected together, at which point the switch is closed. Derive the Vc $($Capacitor Voltage$)$ discharge equation $($express in terms of VF and $).$

$6.$

What is the value of Vc at $20s$ after the switch is opened? $($Unit: V$)$