Why Capacitors Store Half The Charge They Are Given

In summary, the conversation discusses the equations Q=CV and Q=0.5CV for studying capacitors, with the latter being derived from a C-V graph. It is noted that half the charge delivered is stored and the other half is used for energy. The energy equations for capacitors are also mentioned. There is a clarification on the terminology used, with the correct relationships being C=Q/V or Q=CV or V=Q/C. The conversation ends with a friendly welcome to the discussion.
  • #1
Dark Red Rose
1
0
I have been studying capacitors this week and learned two equations. One is Q=CV and the other is Q=0.5CV. The latter equation is derived from C-V graph. From this it shows that half the charge delivered is stored. I am very curious to know where the other half of the charge go and why is the charge stored exactly half of the charge supplied? How is the half of the charge which is not stored used?
 
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  • #2
Dark Red Rose said:
I have been studying capacitors this week and learned two equations. One is Q=CV and the other is Q=0.5CV. The latter equation is derived from C-V graph. From this it shows that half the charge delivered is stored. I am very curious to know where the other half of the charge go and why is the charge stored exactly half of the charge supplied? How is the half of the charge which is not stored used?
The charge stored in a capacitor of capacitance, C, with a potential difference, V, across its plates is Q = CV .

The energy stored in such a capacitor is (1/2)CV2. That doesn't mean that the charge is (1/2)CV.
 
  • #3
Dark Red Rose said:
From this it shows that half the charge delivered is stored. I am very curious to know where the other half of the charge go and why is the charge stored exactly half of the charge supplied? How is the half of the charge which is not stored used?

Replace the word 'charge' in this paragraph with the word 'energy' and you will then have a good question. As Sammy was implying, all of the charge delivered is stored.

P.S. you have an awesome name. and welcome to physics forums!
 
  • #4
You have your terms mixed up
C = Q/V or Q = C x V or V = Q/C...these give the relationships between Q, C and V.
The graph I think you are talking about is Q against V (not C ~ V)
This graph enables you to calculate the ENERGY stored on the capacitor, the ENERGY equations are
E 0.5QV...or 0.5CV^2 or 0.5Q^2/C
 
  • #5


I can explain the reason why capacitors store only half the charge they are given. First, it is important to understand that a capacitor is a device that is used to store electrical energy. It consists of two conductors separated by an insulator, known as a dielectric. When a voltage is applied to the capacitor, it causes a buildup of charge on the two conductors, with one having a positive charge and the other having a negative charge.

Now, let's look at the equation Q=CV, where Q represents the charge stored in the capacitor, C is the capacitance, and V is the voltage applied. This equation tells us that the charge stored in a capacitor is directly proportional to the capacitance and the applied voltage. In other words, the larger the capacitance or the higher the applied voltage, the more charge the capacitor can store.

But why does the Q=0.5CV equation show that only half the charge is stored? This is because the capacitance of a capacitor is not constant, but varies with the amount of charge stored. As the capacitor starts to charge, the capacitance increases, and as it reaches its maximum charge, the capacitance reaches its maximum value. This is known as the dielectric saturation effect.

At this point, the capacitor cannot store any more charge, and any additional charge applied will simply cause the voltage to increase. This is why the Q=CV equation is only valid up to a certain point, after which the capacitor reaches its maximum charge and the equation no longer holds true.

To answer your question about where the other half of the charge goes, it is not lost or used up. It is simply not stored in the capacitor due to the dielectric saturation effect. The other half of the charge still exists in the circuit and can be used in other components or circuits.

In summary, capacitors store only half the charge they are given because of the dielectric saturation effect, which limits the amount of charge a capacitor can hold. The other half of the charge is still present in the circuit and can be used by other components. I hope this explanation helps to clarify your understanding of capacitors.
 

1. Why do capacitors store only half the charge they are given?

Capacitors store charge by accumulating opposite charges on two conductive plates separated by an insulating material. When a capacitor is connected to a power source, it charges up until the potential difference across its plates is equal to the potential difference of the source. However, since the charge on one plate is positive and the charge on the other plate is negative, the total charge stored is only half of what is given by the power source.

2. How does the capacitance affect the amount of charge stored in a capacitor?

The capacitance of a capacitor is directly proportional to the amount of charge it can store. A higher capacitance means that the plates can hold a larger charge, while a lower capacitance means the plates can hold less charge.

3. Can the charge stored in a capacitor be increased?

Yes, the charge stored in a capacitor can be increased by increasing the potential difference across its plates. This can be achieved by connecting the capacitor to a higher voltage power source or by increasing the capacitance of the capacitor itself.

4. Why is it important to discharge a capacitor before handling it?

Capacitors can store a significant amount of charge, which can be dangerous if not handled properly. Discharging a capacitor before handling it ensures that there is no residual charge that can cause harm to the person handling it.

5. How do capacitors store energy?

Capacitors store energy in an electric field between their plates. When a capacitor is connected to a power source, it charges up and stores energy in this electric field. This energy can be released when the capacitor is connected to a circuit, providing a burst of power.

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