5. A capacitor, C, in a circuit with a battery, VB and a resistor R, is...

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5. A capacitor, C, in a circuit with a battery, VB and a resistor R, is being charged by the battery. (a)(5pts) Write down a first order differential equation using Kirchhoff's Loop rule which describes the charge, q(t), on the capacitor and the current, i(t) = dq/dt through the resistor as a function of time. q(t). This equation should be written as an inhomogeneous equation where the inhomogeneous term is the constant voltage, VB (b)(5pts) What is the general solution, qgen(t), of the associated homogeneous equation? Use an arbitrary constant called A. qgen(t) = (c)(5pts) Find the particular solution, of the equation in part (a) above, which we know is a constant. Call it K. Express K using symbols contained is your answer for (a). K = Therefore, using the theorem we discussed in class, the solution of the equation in (a) above can be written as q(t) = qgen(t) + K = (d)(5pts) Find the value of the arbitrary constant, A, which yields the initial condition, q(0) = 0, and then state the particular solution, q(t), for this problem. (e)(5pts) Let the capacitance C = 5.2 10-6 F, the resistance R = 1,500 2 and the battery voltage, Vo = 220 volts. What is the approximate maximum charge, Qmax that can be on the capacitor after a long time? How many minutes will it take for q(t) = 0.90Qmax (e)(5pts) Make Graphs of q(t) and i(t) as functions of the time, t from 0 5. A capacitor, C, in a circuit with a battery, VB and a resistor R, is being charged by the battery. (a)(5pts) Write down a first order differential equation using Kirchhoff's Loop rule which describes the charge, q(t), on the capacitor and the current, i(t) = dq/dt through the resistor as a function of time. q(t). This equation should be written as an inhomogeneous equation where the inhomogeneous term is the constant voltage, VB (b)(5pts) What is the general solution, qgen(t), of the associated homogeneous equation? Use an arbitrary constant called A. qgen(t) = (c)(5pts) Find the particular solution, of the equation in part (a) above, which we know is a constant. Call it K. Express K using symbols contained is your answer for (a). K = Therefore, using the theorem we discussed in class, the solution of the equation in (a) above can be written as q(t) = qgen(t) + K = (d)(5pts) Find the value of the arbitrary constant, A, which yields the initial condition, q(0) = 0, and then state the particular solution, q(t), for this problem. (e)(5pts) Let the capacitance C = 5.2 10-6 F, the resistance R = 1,500 2 and the battery voltage, Vo = 220 volts. What is the approximate maximum charge, Qmax that can be on the capacitor after a long time? How many minutes will it take for q(t) = 0.90Qmax (e)(5pts) Make Graphs of q(t) and i(t) as functions of the time, t from 0