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:


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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