Question

A certain capacitor, in series with a resistor, is being charged. At the end of 25 ms its charge is half the final value. The time constant for the process is about:

Answer 1

Answer:

  τ = 36 10⁻³ s

Explanation:

The charge of a circuit Rc is given by the expression

          q = q₀ (1 - $e^{-t/ \tau }$)

          q / q₀ = 1 - e^{-t/  \tau }

in this exercise they indicate that

          q / q₀ = ½

for a time t = 25 10⁻³ s

we substitute

          ½ = 1 - $e^{- 25 \ 10^{-3} / \tau}$

          e^{- 25 \ 10^{-3} /  \tau} =  1 -½

         - 25 10⁻³ /τ = ln 0.5

         -25 10⁻³ / ln 0.5 = τ

         τ = 36 10⁻³ s