A capacitance C charged to a potential difference V is discharged by connecting its plates through a resistance R. Find the heat dissipated in one time constant after the connections are made. Do this by calculating ∫i2R dt and also by finding the decrease in the energy stored in the capacitor.
Concepts/Formulas Used:
Energy dissipated by a resistor :
A resistor of resistance R with current I through it, dissipates energy U given by:
in time Δt.
Its power is given by:
Current when capacitor is discharging:
A capacitor of capacitance C is being charged through a resistance R , the current through the circuit is given by:
Where I0 is the initial current.
Energy stored by capacitor:
For a capacitor of capacitance C , with charge Q, and potential difference V across it, the energy stored is given by:
Discharging a capacitor:
A capacitor of capacitance C is connected in series with a resistor of resistance R and a switch. Before the switch is closed, it has charge Qi . If the switch is closed at t = 0, then at any time t, the charge on the capacitor is given by:
where 
The initial energy of the capacitor,
As the capacitor is discharged, it looses Charge ,and the potential difference across it also decreases.
Note that 
Now, at t= τ,
The energy lost is dedicated as heat and is equal to:
Now let us find the energy dissipated by another method:
Substituting 
,
Note that 
and 
Both ways give us the same result!