This problem deals with the RC circuit shown here, containing a resistor (R ohms), a capacitor (C farads), a switch, a source of emf, but no inductor. The charge Q = Q(t) on the capacitor at time t satisfies the following linear first-order differential equation. dQ 1 R+ Q = E(t) C dt Note that I(t) = Q'(t). Answer parts (a) and (b). Switch The charge is Q(t) = (Type an exact answer.) R C (a) Find the charge Q(t) and the current I(t) in the RC circuit if E(t) = V₁ (a constant voltage supplied by a battery) and the switch is closed at time t=0, so that Q(0) = 0.
This problem deals with the RC circuit shown here, containing a resistor (R ohms), a capacitor (C farads), a switch, a source of emf, but no inductor. The charge Q = Q(t) on the capacitor at time t satisfies the following linear first-order differential equation. dQ 1 R+ Q = E(t) C dt Note that I(t) = Q'(t). Answer parts (a) and (b). Switch The charge is Q(t) = (Type an exact answer.) R C (a) Find the charge Q(t) and the current I(t) in the RC circuit if E(t) = V₁ (a constant voltage supplied by a battery) and the switch is closed at time t=0, so that Q(0) = 0.
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Transcribed Image Text:This problem deals with the RC circuit shown here, containing a resistor (R ohms), a capacitor (C
farads), a switch, a source of emf, but no inductor. The charge Q = Q(t) on the capacitor at time t
satisfies the following linear first-order differential equation.
dQ 1
R- +
dt
с
Note that I(t) = Q'(t). Answer parts (a) and (b).
= E(t)
Q=
E
The charge is Q(t) =
(Type an exact answer.)
Switch
R
с
(a) Find the charge Q(t) and the current I(t) in the RC circuit if E(t) = V₁ (a constant voltage supplied by a battery) and the switch is closed at
time t= 0, so that Q(0) = 0.
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