5. The electrical circuit below consists of a battery with time-varying voltage V(t), a resistorwith resistance R = 20, and a capacitor with capacitance C = 3F:V (t)RMRCAccording to the theory of electric circuits, the voltage ve(t) across the capacitor satisfies theODEdvedtCv (t) = {+ Vc = V(t).Suppose the battery is turned on at t = 0 seconds and held at 5 Volts up to time t = 3seconds, and then is turned off, so the voltage is5V + € [0,3)OV t≥ 3.(a) Find the voltage in the capacitor as a function of time t, assuming there is initially novoltage in the capacitor. (b) What is the voltage in the capacitor at time t = 6 seconds?(Hint: you might need to solve 2 ODEs, one for t€ [0,3), the other for t > 3).

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Answered: (a) Find the voltage in the capacitor…

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(a) Find the voltage in the capacitor as a function of time t, assuming there is initially no voltage in the capacitor. (b) What is the voltage in the capacitor at time t = 6 seconds?