In an RC circuit, how many time constants must elapse if an initially uncharged capacitor is to reach 80% of its final potential difference

1.6 time constants must elapse

Explanation:

voltage on a cap, charging is given as

v = v₀[1–e^(–t/τ)]

Where R is resistance in ohms,

C is capacitance in farads

t is time in seconds

RC = τ = time constant

v = v₀[1–e^(–t/τ)]

1–e^(–t/τ) = 0.8

e^(–t/τ) = 0.2

–t/τ = –1.609

t = 1.609τ