After how many time constants has the voltage across a discharging capacitor decayed to 0.85{\rm \\%} of its initial value?

After voltage across the capacitor will be 0.85 % of the initial voltage across the capacitor

Explanation:

Let initially voltage across capacitor is

After discharging the voltage across the capacitor is .85% of its initial voltage

So final voltage

We know that voltage across capacitor is given by

So

So after voltage across the capacitor will be 0.85 % of the initial voltage across the capacitor

Time constant of capacitive circuit is equal to the ratio of resistance and capacitance

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