Answer:
The current in the circuit at a time interval of τ seconds after the switch has been closed is 0.123 A
Explanation:
The time constant for an R and C in series circuit is given by τ = RC.
R = 3000 ohms, C = 0.5 × 10⁻⁶ F = 5.0 × 10⁻⁷ F
τ = 3000 × 5 × 10⁻⁷ = 0.015 s
The voltage across a capacitor as it charges is given be
V(t) = Vs (1 - e⁻ᵏᵗ)
where k = 1/τ
At the point when t = τ, the expassion becomes
V(t = τ) = 1000 (1 - e⁻¹) = 0.632 × 1000 = 632 V
Current flows as a result of potential difference,.
Current in the circuit at this time t = τ is given by
I = (Vs - Vc)/R
Vs = source voltage = 1000 V
Vc = Voltage across the capacitor = 632 V
R = 3000 ohms
I = (1000 - 632)/3000 = 0.123 A
