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The timing of an intermittent windshield wiper is controlled by a variable resistor in a resistor-capacitor circuit. A 12 volt battery charges the capacitor. When the voltage across the capacitor reaches 10 volts, a switch closes to discharge the capacitor and energize the electric motor that moves the windshield wiper. Then the process repeats with the battery charging the capacitor again.
The voltage across the capacitor follows the equation dv 1 1 + V = :Vb dt RC RC Where R = 30,000 ohms (resistance), C = 0.0001 F (capacitance), v= 12 V (battery voltage). Solve the ODE using the methods from 2.2 or 2.3 and write v as a function of time (show all your work). Also, plot your solution v(t) with the initial condition v = 0 (any plotting software is fine). Note that the units given are consistent, so there is no need to do any unit conversions to use the equation.