In an RC series circuit, ε = 12.0 V, R = 1.25 MΩ, and C = 1.42 µF. (a) Calculate the time constant. (b) Find the maximum charge that will appear on the capacitor during charging. (c) How long does it take for the charge to build up to 8.78 µC?

a, 1.775s

b, 17.04μC

c, 1.28s

Explanation:

Given

R = 1.25MΩ

C = 1.42µF

ε = 12.0 V

q = 8.78 µC

Time constant, τ = RC

τ = (1.25*10^6) * (1.42*10^-6)

τ = 1.775s

q• = εC

q• = 12 * 1.42*10^-6

q• = 17.04*10^-6C

q• = 17.04μC

Time t =

q = q• [1 - e^ (t/τ) ]

t = τIn[q• / (q•-q) ]

t = 1.775In[17.04μC / (17.04μC-8.78μC) ]

t = 1.775In (2.06)

t = 1.775*0.723

t = 1.28s