Question

A charged capacitor is discharged through a resistance. The time constant of the circuit is eta. Then the value of time constant for the power dissipated through the resistance will be

Answer 1

☆During discharge the current though resistance is i=i0e−t/η where η= time constant.

Power dissipation through resistor R is P=i2R=i02e−2t/ηR=P0e−t/(η/2) 

Thus time constant becomes 2η

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Answer 2

Given :-

Time constant = η

To Find :-

The value of time constant for the power dissipated

Solution:-

We know that the current

i = $i_{0}e^{\frac{-t}{n} }$

and

Power P = i²R

Now putting the value of i in above equation.

P = $i_{0}^{2}(e^{\frac{-t}{n} })^{2}xR$

P = $i_{0}^{2}R(e^{\frac{-2t}{n} })$

P = $P_{0}e^{\frac{-t}{\frac{n}{2} } }$     Where  $P_{0} = i_{0}^{2}R$

Then the value of time constant for power dissipated through the resistance will be η/2 i.e  time constant will be $\frac{n}{2}$