Q104 You have the following circuit: When a charged capacitor is linked to an inductor, it induces a current to pass through the inductor, depleting the capacitor's charge until it is entirely discharged. The current flowing in the inductor, in return, charges up the capacitor until it becomes fully charged. If Q(t) denotes the charge on the capacitor at time t, and I represents the current, then. dQ I= L=dI Lud! , Q=0 dt dt In the case that the resistance in the circuit is zero, Charge Q and current I would satisfy the differential equation shown below: d²Q Ldt² inductor In which L denotes the inductance and C denotes the capacitance, so the following equation can be made; L-da 9-0 dQ dt² Q(t)=_ HH capacitor In the same way that a spring can experience a damping force influencing its movement, a circuit can also have a similar effect introduced by the resistor. The resistor, with a resistance denoted by R, plays a role in this process. dQ *Rd 2 +&Q=0 m b) Q(0)=2 & Q'(0)=0 Q(t)= resistor Assuming that you know R=(1/2)ohm, L=1 henry, and C=16 farads determine the formula for the charge when: Write your answers in the blanks provided below. a) Q(0)=0 & Q'(0)=2
Q104 You have the following circuit: When a charged capacitor is linked to an inductor, it induces a current to pass through the inductor, depleting the capacitor's charge until it is entirely discharged. The current flowing in the inductor, in return, charges up the capacitor until it becomes fully charged. If Q(t) denotes the charge on the capacitor at time t, and I represents the current, then. dQ I= L=dI Lud! , Q=0 dt dt In the case that the resistance in the circuit is zero, Charge Q and current I would satisfy the differential equation shown below: d²Q Ldt² inductor In which L denotes the inductance and C denotes the capacitance, so the following equation can be made; L-da 9-0 dQ dt² Q(t)=_ HH capacitor In the same way that a spring can experience a damping force influencing its movement, a circuit can also have a similar effect introduced by the resistor. The resistor, with a resistance denoted by R, plays a role in this process. dQ *Rd 2 +&Q=0 m b) Q(0)=2 & Q'(0)=0 Q(t)= resistor Assuming that you know R=(1/2)ohm, L=1 henry, and C=16 farads determine the formula for the charge when: Write your answers in the blanks provided below. a) Q(0)=0 & Q'(0)=2
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Transcribed Image Text:Q104
You have the following circuit:
When a charged capacitor is linked to an inductor, it
induces a current to pass through the inductor, depleting
the capacitor's charge until it is entirely discharged. The
current flowing in the inductor, in return, charges up the
capacitor until it becomes fully charged. If Q(t) denotes the
charge on the capacitor at time t, and I represents the
current, then.
dQ
I=
L-10-9-0
dt²
dt
In the case that the resistance in the circuit is zero, Charge Q and current I would satisfy the differential
equation shown below:
2-0
d²Q
Ldt²
L=dI
dt
In which L denotes the inductance and C denotes the capacitance, so the following equation can be made;
2=0
inductor
Q(t)=_
HH
capacitor
In the same way that a spring can experience a damping force influencing its movement, a circuit can also
have a similar effect introduced by the resistor. The resistor, with a resistance denoted by R, plays a role in
this process.
dQ
*Rd 2 + &Q=0
m
b) Q(0)=2 & Q'(0)=0
Q(t)=
resistor
Assuming that you know R=(1/2)ohm, L=1 henry, and C=16 farads determine the formula for the charge
when:
Write your answers in the blanks provided below.
a) Q(0)=0 & Q'(0)=2
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