Assume I have a capacitor with capacity \$C\$ and is charged to a voltage level \$V_a\$ and then discharged.
1) During discharge it dissipates \$E\$ joules of energy. What is the equation to find the final voltage \$V_b\$ of the capacitor after \$E\$ joules have been discharged ?
2) After the same capacitor discharges and reaches \$V_b\$, we re-charge it up to \$V_a\$ again. Assume the charging current is (\$I\$) (Amps). What is the equation to find how much time (\$t\$) it take for the capacitor to charge from \$V_b\$ to \$V_a\$ ?
I am looking for equations without resistance (\$R\$) involved, as I do not know the resistance of the circuit (MCU based), but only the energy consumption of the load.
I googled for these equations, but could not come up with a specific answer. I have learnt these equations in school/university, but have forgotten now.