How Many Time Constants Will Elapse before the Charge on a Capacitors Falls to 0.1% of Its Maximum Value in a Discharging Rc Circuit? - Physics

Sum

How many time constants will elapse before the charge on a capacitors falls to 0.1% of its maximum value in a discharging RC circuit?

The decay of charge across a capacitor,

\[q = Q e^{- \frac{t}{RC}}\]

Here, q = 0.1 % and Q = 1 × 10⁻³ Q

⇒ 1 × 10⁻³ Q = \[Q e^{- \frac{t}{RC}}\]

\[\Rightarrow e^{- \frac{t}{RC}}=10^{-3}\]

\[\Rightarrow \frac{t}{rC} = - \left( - 6 . 9 \right) = 6 . 9\]

Let t = nRC

\[\Rightarrow \frac{nRC}{RC} = 6 . 9\]

\[ \Rightarrow n = 6 . 9\]

Concept: Energy Stored in a Capacitor

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Chapter 10 Electric Current in Conductors
Q 71 | Page 203