Answer :

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!


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