Charging and Discharging of a Capacitor in R-C Circuit

The equation for the discharge current at any instant of time of $RC$ circuit is

Derive the equation for decreasing current while discharging a capacitor in $RC$ circuit. 

A resistor and a capacitor are connected as shown in the figure. The capacitor is originally given a charge of $10.0 \mu C$ and then discharged by closing the switch at $t=0$. What is the current at this time?

A resistor and a capacitor are connected as shown in the figure. The capacitor is originally given a charge of $5.0 \mu C$ and then discharged by closing the switch at $t=0$. What is the current at this time?

The plates of a $50 \mu F$ capacitor charged to $400 \mu C$ are connected through a resistance of $1.0 k\Omega$. Find the charge remaining on the capacitor $1 s$ after the connection is made.

A resistor and a capacitor are connected as shown in the figure. The capacitor is originally given a charge of $5.0 \mu C$ and then discharged by closing the switch at $t=0$. At what time will the charge be equal to $0.50 \mu C$?

A capacitor of capacitance $10 \mu F$ is connected to a resistance $2 \Omega$ and a battery of e.m.f. $5 V$ of negligible internal resistance. After $20 \mu s$ of completing the circuit, find power dissipated as heat..

A capacitor of capacitance $10 \mu F$ is connected to a resistance $2 \Omega$ and a battery of e.m.f. $5 V$ of negligible internal resistance. After $20 \mu s$ of completing the circuit, find power delivered by the battery.

Show graphically how charge on a capacitor and current through the capacitor varies with time during charging and discharging of the capacitor.

In rectification, the capacitor is connected serially to the load.

The charge on a capacitor in two different $RC$ circuits $1$ and $2$ are plotted as shown in the figure. Choose the correct statement(s) related to the two circuits.

What is the purpose of a capacitor in the rectifier circuit? 

Why does current in a steady state not flow in a capacitor connected across a battery? However, momentary current does flow during charging or discharging of the capacitor. Explain?

Derive the expression of current as a function of time during the charging of the capacitor in the $RC$ circuit.

Cotyledons are also called-