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3. The figure below shows an RC circuit. (a) If the initial charge in the circuit is Q(0) = 0, show that the differential equation governing the charge is given by: dQ Q + dt RC (1) (b) If Vi(t) = V₁, constant for t > 0, determine the charge Q(t) as a function of t. Use integrating factors method (c) If the voltage is given by Vi V₂(t)=V₂ = wwww R Vi(t) R 0 t<0 0T determine Q(t) using integrating factors. (d) If Vi(t) = V₂ sin wt, determine Q(t). Use both integrating factors and the method of undetermined coefficients. C= (2) Figure 1: RC circuit

3. The figure below shows an RC circuit. (a) If the initial charge in the circuit is Q(0) = 0, show that the differential equation governing the charge is given by: dQ Q + dt RC (1) (b) If Vi(t) = V₁, constant for t > 0, determine the charge Q(t) as a function of t. Use integrating factors method (c) If the voltage is given by Vi V₂(t)=V₂ = wwww R Vi(t) R 0 t<0 0T determine Q(t) using integrating factors. (d) If Vi(t) = V₂ sin wt, determine Q(t). Use both integrating factors and the method of undetermined coefficients. C= (2) Figure 1: RC circuit

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3. The figure below shows an RC circuit. (a) If the initial charge in the circuit is Q(0) = 0, show that the differential equation governing the charge is given by: (1) (b) If Vi(t) = V₁, constant for t > 0, determine the charge Q(t) as a function of t. Use integrating factors method (c) If the voltage is given by dQ Q + dt RC Vi V₂(t)= = = = wwww R Vi(t) 0 t < 0 Vi 0<t<T 0 t > T R determine Q(t) using integrating factors. (d) If V (t) = V₂ sin wt, determine Q(t). Use both integrating factors and the method of undetermined coefficients. Figure 1: RC circuit (2)
Transcribed Image Text:3. The figure below shows an RC circuit. (a) If the initial charge in the circuit is Q(0) = 0, show that the differential equation governing the charge is given by: (1) (b) If Vi(t) = V₁, constant for t > 0, determine the charge Q(t) as a function of t. Use integrating factors method (c) If the voltage is given by dQ Q + dt RC Vi V₂(t)= = = = wwww R Vi(t) 0 t < 0 Vi 0<t<T 0 t > T R determine Q(t) using integrating factors. (d) If V (t) = V₂ sin wt, determine Q(t). Use both integrating factors and the method of undetermined coefficients. Figure 1: RC circuit (2)
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