Capacitance of a conductor

In summary, the capacitance C of a conductor is a constant relationship between charge Q and potential V. The potential is linear with the charge on the conductor, not the charge that is added. This means that the proportionality between Q and V is constant, but the relationship between ΔQ and ΔW is not. The capacitance depends on physical properties and dimensions, not electrical properties. Q and V do not have to be linear, as long as the ratio between them remains constant. When adding new charges to the conductor, the potential does not depend on the charge already there, but rather on the ratio of Q/C, which is constant.
  • #1
Higgsono
93
4
The capacitance C of a conductor is given to be a constant relationship between charge Q and potential V of the conductor given by Q = CV.
But how can C be a constant? Because the potential of the conductor will not be a linear relationship of the charge that I add. THe more charge there is on the conductor already, the more work is needed to add additional charge. Hence the potential I add by bringing new charges to the conductor must depend on the charge already there.

What is it that I don't understand?
 
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  • #2
Higgsono said:
Because the potential of the conductor will not be a linear relationship of the charge that I add.
The potential is linear with the charge that is on the conductor, not the charge that is added. I.e. ##V## is proportional to ##Q## not ##\Delta Q##
 
  • #3
Dale said:
The potential is linear with the charge that is on the conductor, not the charge that is added. I.e. ##V## is proportional to ##Q## not ##\Delta Q##

huh? Q and V are not constants. I must be able to double the charge and the relation should be the same right?
 
  • #4
Higgsono said:
huh? Q and V are not constants. I must be able to double the charge and the relation should be the same right?
Yes, the proportionality between ##Q## and ##V## is constant, but what you are describing in your text is the relationship between ##\Delta Q## and ##\Delta W##. ##\Delta Q\ne Q## and ##\Delta W \ne V##
 
  • #5
Remember that C is a physical quantity. Remember back to the simple capacitance days and how two plates make a capacitor. The capacitance depends on dimensions and material properties. It does not depend on electrical properties. It is a constant as long as the materials and the physical dimensions don't change.

As for the charge and voltage, capacitance is the ratio of the two, C=Q/V; therefore Q and V don't have to be linear, they can follow any line as long as the ratio between them remains constant.

If you want to look at the different lines that Q and V follow, look at charging and discharging a capacitor at constant current versus constant voltage/resistance.
 
  • #6
Let’s try it more quantitatively
Higgsono said:
Because the potential of the conductor will not be a linear relationship of the charge that I add.
That is correct. ##V \propto Q## not ##V \propto dQ##

Higgsono said:
THe more charge there is on the conductor already, the more work is needed to add additional charge.
Yes, ##dW/dQ=f(Q)## where ##df/dQ>0##

Specifically
##dW/dt=P=IV=V \; dQ/dt##
##dW/dQ = V = Q/C =f(Q)##
So ##df/dQ =1/C>0##

Higgsono said:
Hence the potential I add by bringing new charges to the conductor must depend on the charge already there.
No, it does not follow. Instead ##dV/dQ = 1/C##
 

1. What is capacitance of a conductor?

Capacitance of a conductor is a measure of its ability to store an electrical charge. It is defined as the ratio of the amount of charge stored on a conductor to the potential difference (voltage) across the conductor.

2. How is capacitance calculated?

The capacitance of a conductor is calculated by dividing the charge stored on the conductor by the potential difference across it. It can also be calculated by multiplying the permittivity of the material by the surface area of the conductor and dividing by the distance between the plates.

3. What factors affect the capacitance of a conductor?

The capacitance of a conductor is affected by several factors, including the size and shape of the conductor, the distance between the plates, and the type of material used. It also depends on the dielectric constant of the material between the plates.

4. How does capacitance change with distance?

The capacitance of a conductor is inversely proportional to the distance between the plates. As the distance increases, the capacitance decreases. This is because a larger distance between the plates means a smaller electric field, which results in less charge being stored.

5. What are some real-life applications of capacitance?

Capacitance has many practical applications, such as in electronic circuits, power factor correction, and energy storage. It is also used in devices such as capacitors, sensors, and touch screens. Capacitance is also important in high-voltage power transmission and in the functioning of the human body's nervous system.

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