What is the Charge on the Capacitor in a Circuit After Switching Positions?

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In summary, the conversation is about finding the charge on a capacitor in a circuit after a switch is changed from position a to position b at t=0s. The equations used are (1) C=Q/V, (2) V=IR, (3) q=Qinit.(1-e^(-t/τ)), and (4) τ=RC. The solution involves solving for Q using equations (1) and (2), then substituting equation (4) into equation (3) to find the charge on the capacitor at t=50s. There may be an error in equation (3) and it is suggested to check the values at t=0 and t=infinity to confirm the solution.
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etown
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Homework Statement


The switch in the figure has been in position a for a long time. It is changed to position "b" at t=0s. What is the charge Q on the capacitor at t=50s?

(zeros denote empty space in the circuit)

|----(a)0000(b)--------- |
|00000\00000000000000|
9V00000\000000000000|
|00000000|00000000025 Ohm
|00000004uF000000000|
|________|___________|


Homework Equations


(1) C=Q/V
(2) V=IR
(3) q=Qinit.(1-e^(-t/τ))
(4) τ=RC


The Attempt at a Solution


Ok, so I start by using (1) to find that Q=36uC, then I use (2) to find that I=.36A, but after that is where i encounter problems. I am trying to use (3) to find the charge but it's not giving me the right answer. I'm not sure how to use (4), what is that formula telling me, and am i doing everything right?

The answer should be 22uC
 
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  • #2
Notice that in equation (3) you have the parameter 1/T, this is exactly what equation (4) is telling you. Try substituting (4) into (3) and seeing if you get the right solution.
 
  • #3
You may want to take a closer look at your equation (3). In particular, check what the function yields for t = 0 and in the limit as t --> infinity. Does it correspond to what you intuitively feel should happen to the charge on the capacitor?
 

What is a capacitor and how does it work?

A capacitor is an electronic component that stores electrical energy in the form of an electric field. It consists of two conductive plates separated by an insulating material, known as a dielectric. When a voltage is applied to the capacitor, one plate becomes positively charged while the other becomes negatively charged. This creates an electric field between the plates, storing energy that can be released when needed.

What is the purpose of a capacitor in a circuit?

Capacitors have several important functions in a circuit. They can act as temporary energy storage, smoothing out fluctuations in voltage and current. They can also block DC signals while allowing AC signals to pass through, acting as a high-pass filter. Additionally, capacitors can be used to store and release energy in timing circuits, or as part of an oscillator circuit.

How do you calculate the capacitance of a capacitor?

The capacitance of a capacitor is determined by the physical properties of the capacitor, such as the area of the plates, the distance between them, and the type of dielectric material used. The formula for capacitance is C=ε0A/d, where C is capacitance, ε0 is the permittivity of free space, A is the area of the plates, and d is the distance between them. Capacitance is measured in units of Farads (F).

What is the difference between a polarized and non-polarized capacitor?

A polarized capacitor has a designated positive and negative terminal, and must be connected in the correct orientation in a circuit. These types of capacitors are typically used in DC circuits. Non-polarized capacitors, on the other hand, can be connected in either direction and are suitable for use in AC circuits. They do not have a designated positive or negative terminal.

How do capacitors affect the frequency response of a circuit?

In a circuit, capacitors have a reactance, or opposition to AC signals, that varies with frequency. This means that the capacitance of a capacitor affects the flow of AC signals through the circuit. At low frequencies, capacitors have a high reactance, which decreases as the frequency increases. This can be used to filter out certain frequencies and shape the overall frequency response of the circuit.

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