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If L-1 henry, R=1 ohm, and C= 4 farads, find a formula for the charge when (a) Q(0) = 0 and Q (0) - 5: Q(t)= 4e^(-1/2) L L d²Q dt² d²Q dt² Then, just as as a spring can have a damping force which affects its motion, so can a circuit; this is introduced by the resistor, so that if the resistance of the resistor is R ㅎㅇ - + +R 0. dt = 0,

If L-1 henry, R=1 ohm, and C= 4 farads, find a formula for the charge when (a) Q(0) = 0 and Q (0) - 5: Q(t)= 4e^(-1/2) L L d²Q dt² d²Q dt² Then, just as as a spring can have a damping force which affects its motion, so can a circuit; this is introduced by the resistor, so that if the resistance of the resistor is R ㅎㅇ - + +R 0. dt = 0,

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This problem concerns the electric circuit shown in the figure below. where C is the capacitance and L is the inductance, so A charged capacitor connected to an inductor causes a current to flow through the inductor until the capacitor is fully discharged. The current in the inductor, in turn, charges up the capacitor until the capacitor is fully charged again. If Q(t) is the charge on the capacitor at time t, and I is the current, then dQ dt If the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation dI 'dt + If L=1 henry, R=1 ohm, and C = 4 farads, find a formula for the charge when (a) Q (0) = 0 and Q (0) = 5: Q(t)= 4e^(-1/2) Capacitor L (b) Q(0) = 5 and Q (0) = 0: Q(t) = Resistor mamm DOUVID Inductor L I= 8²0+0=0 d²Q dt2 Then, just as as a spring can have a damping force which affects its motion, so can a circuit; this is introduced by the resistor, so that if the resistance of the resistor is R d²Q dQ dt +R dt² +9=0. www = 0,
Transcribed Image Text:This problem concerns the electric circuit shown in the figure below. where C is the capacitance and L is the inductance, so A charged capacitor connected to an inductor causes a current to flow through the inductor until the capacitor is fully discharged. The current in the inductor, in turn, charges up the capacitor until the capacitor is fully charged again. If Q(t) is the charge on the capacitor at time t, and I is the current, then dQ dt If the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation dI 'dt + If L=1 henry, R=1 ohm, and C = 4 farads, find a formula for the charge when (a) Q (0) = 0 and Q (0) = 5: Q(t)= 4e^(-1/2) Capacitor L (b) Q(0) = 5 and Q (0) = 0: Q(t) = Resistor mamm DOUVID Inductor L I= 8²0+0=0 d²Q dt2 Then, just as as a spring can have a damping force which affects its motion, so can a circuit; this is introduced by the resistor, so that if the resistance of the resistor is R d²Q dQ dt +R dt² +9=0. www = 0,
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