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Question:

At time t=0, a battery of 10V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 volt?

Solution:

Equation of charging of capacitor V = V₀(1 - e⁻ᵗ/ReqCeq)
Req = 2 × 2/(2 + 2) = 1 MΩ
Ceq = 2 + 2 = 4 μF
V = V₀(1 - e⁻ᵗ/⁴)
where V₀ = 10V and V = 4V
⇒ 4 = 10(1 - e⁻ᵗ/⁴)
⇒ e⁻ᵗ/⁴ = 3/5
⇒ t/4 = ln5 - ln3
⇒ t = 4(ln5 - ln3) ≈ 2 sec