(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?
(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?
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Transcribed Image Text:5. The electrical circuit below consists of a battery with time-varying voltage V(t), a resistor
with resistance R = 20, and a capacitor with capacitance C = 3F:
V (t)
R
M
RC
According to the theory of electric circuits, the voltage ve(t) across the capacitor satisfies the
ODE
dve
dt
C
v (t) = {
+ Vc = V(t).
Suppose the battery is turned on at t = 0 seconds and held at 5 Volts up to time t = 3
seconds, and then is turned off, so the voltage is
5V + € [0,3)
OV t≥ 3.
(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?
(Hint: you might need to solve 2 ODEs, one for t€ [0,3), the other for t > 3).
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