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Problem 2: Charging of a capacitor In the circuit shown in the figure, at t = 0 there is no charge on the capacitor and the switch S is closed. Express your results in terms of V₁, R₁, R₂, and C. (a) We first consider what happens att → ∞. What is the current in the capacitor? What is the po- tential difference on R₂ and the charge on the capacitor, Q? (b) Now for t > 0, derive the differential equation governing the time evolution of the capacitor's charge Q(t). (c) Solve it to determine Q(t) for t > 0 and plot/sketch it as a function of t. R₁ C R₂ www

Problem 2: Charging of a capacitor In the circuit shown in the figure, at t = 0 there is no charge on the capacitor and the switch S is closed. Express your results in terms of V₁, R₁, R₂, and C. (a) We first consider what happens att → ∞. What is the current in the capacitor? What is the po- tential difference on R₂ and the charge on the capacitor, Q? (b) Now for t > 0, derive the differential equation governing the time evolution of the capacitor's charge Q(t). (c) Solve it to determine Q(t) for t > 0 and plot/sketch it as a function of t. R₁ C R₂ www

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Problem 2: Charging of a capacitor In the circuit shown in the figure, at t = 0 there is no charge on the capacitor and the switch S is closed. Express your results in terms of V₁, R₁, R₂, and C. (a) We first consider what happens at t → ∞. What is the current in the capacitor? What is the po- tential difference on R₂ and the charge on the capacitor, Q? (b) Now for t > 0, derive the differential equation governing the time evolution of the capacitor's charge Q(t). R₁ V₂ C R₂ www (c) Solve it to determine Q(t) for t > 0 and plot/sketch it as a function of t. (e) What is the maximum current, imax, in the capacitor during its charge? = (f) Calculate Q and imax for a typical flash capacitor circuit with V₁ = 300 V, R₁ = 1022, R₂ 10M2, C = 100μF.
Transcribed Image Text:Problem 2: Charging of a capacitor In the circuit shown in the figure, at t = 0 there is no charge on the capacitor and the switch S is closed. Express your results in terms of V₁, R₁, R₂, and C. (a) We first consider what happens at t → ∞. What is the current in the capacitor? What is the po- tential difference on R₂ and the charge on the capacitor, Q? (b) Now for t > 0, derive the differential equation governing the time evolution of the capacitor's charge Q(t). R₁ V₂ C R₂ www (c) Solve it to determine Q(t) for t > 0 and plot/sketch it as a function of t. (e) What is the maximum current, imax, in the capacitor during its charge? = (f) Calculate Q and imax for a typical flash capacitor circuit with V₁ = 300 V, R₁ = 1022, R₂ 10M2, C = 100μF.
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