A capacitor with initial charge q0 is discharged through a resistor. What multiple of the time constant τ gives the time the cap

Question

Stolb23

2 days ago

9

A capacitor with initial charge q0 is discharged through a resistor. What multiple of the time constant τ gives the time the cap

acitor takes to lose
(a) the first 1/8-th of its charge
(b)7/8-th of its charge?

Physics

1 answer:

Maru [3.2K] · Answer 1 · 2026-04-07T01:36:42+03:00

a) 0.13*τ; b) 2.08*τ. To describe the discharging process of a capacitor through a resistor, consider the following: Q(t) = Qo * exp(-t/τ) to signify a loss of 1/8 of its charge. In this scenario, Q(t) = 7/8 * Qo = 7/8 * exp(-t/τ). By rearranging, we have ln(7/8)*τ = -t, thus t = -ln(7/8)*τ = 0.13. For a loss of 7/8 of its charge, we use Q(t) = 1/7 * Qo * exp(-t/τ), leading to t = -ln(1/8)*τ = 2.08.