Capacitors: charge, potential difference and stored energy

In summary, the voltage is the energy per unit charge needed to move a charge from point p(1) to point p(2). The student must expend energy per unit charge in moving some charge q only if there is an electric field between the points.
  • #1
CIERAcyanide
9
0

Homework Statement



The 50Volts is going through 3 capacitors.
C1 = 4.0 µF, C2 = 8.0 µF, and C3 = 9.0 µF,

The URL below is the image of how the capacitors are connected:
http://www.webassign.net/hrw/26_27.gif

For each capacitor i need to find the charge, the potential difference and the stored energy.

Homework Equations



CV = Q

The Attempt at a Solution


I really don't understand what potential difference is, and I'm not sure what the problem asks for with the stored energy.
I tried CV = Q for the charge of C1 and got 4E-6 * 50 = 2E-4, which is wrong.
 
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  • #2
CIERAcyanide said:

Homework Statement



The 50Volts is going through 3 capacitors.
C1 = 4.0 µF, C2 = 8.0 µF, and C3 = 9.0 µF,

The URL below is the image of how the capacitors are connected:
http://www.webassign.net/hrw/26_27.gif

For each capacitor i need to find the charge, the potential difference and the stored energy.

Homework Equations



CV = Q

The Attempt at a Solution


I really don't understand what potential difference is, and I'm not sure what the problem asks for with the stored energy.
I tried CV = Q for the charge of C1 and got 4E-6 * 50 = 2E-4, which is wrong.

Remember that a capacitor is a break in the circuit. Capacitors in parallel can store a lot more charge than two in series, because the parallel combination allows each plate to fill up with its "rated" charge. In the series combination, the break in the circuit prevents this simple process. Instead, charge is stored on the first plate the voltage source comes in contact with and then charge departs the bottom plate toward the second capacitor's first plate. The second capacitor's second plate then departs charge toward to voltage source allowing for an apparent current (though no charge actually flows THROUGH a capacitor). Specific to this problem, all of the charge depleted from the voltage source due to the equivalent capacitance, Ceq, must be stored on the first two capacitors that are in parallel. The third capacitor holds the same charge as the two in parallel do (because it only receives charge out of the departure of charge from the first two capacitors which is equal to the stored charge on the first capacitor's plates)

Voltage is the energy per unit charge needed to move a charge from point p(1) to point p(2). A person must expend energy per unit charge in moving some charge q only if there is an electric field between the points. (Remember, f = Eq. If E = 0, f = 0 and w = 0).

The mechanical analog to voltage usually helps students visualize the concept:
gravitational potential energy due to a gravitational field is mgh where m is the measurement of the material's sensitivity to the field's tendency, g is the field, and h is the distance over which the constant field acts. If both sides were divided by mass, we would arrive to the never used but now dubbed gravitational potential (work per mass) -- gh.

Similarly, electric potential energy is qEd where q is the measurement of the material's sensitivity to the field's tendency, E is the field, and d is the distance over which the constant field acts. If both sides are divided by charge, we would arrive to the always used electric potential (i.e. voltage, work per charge) -- Ed.
 
Last edited:
  • #3
Thank you so much! I really appreciate your in depth response; it cleared up a lot.
 

1. What is a capacitor?

A capacitor is an electronic component that is used to store electrical energy. It consists of two conductive plates separated by an insulating material, called a dielectric.

2. How does a capacitor store charge?

When a potential difference is applied across the two plates of a capacitor, electrons accumulate on one plate and are depleted from the other plate. This creates an electric field between the plates, which stores the charge.

3. What is potential difference in relation to capacitors?

Potential difference, also known as voltage, is the difference in electric potential energy per unit charge between the two plates of a capacitor. It is what causes charge to flow from one plate to the other and is measured in volts (V).

4. How is the energy stored in a capacitor?

The energy stored in a capacitor is equal to the product of half the capacitance (C) and the square of the potential difference (V), or E = 1/2 CV^2. This means that the energy stored in a capacitor is directly proportional to its capacitance and the square of the potential difference applied.

5. How do capacitors differ from batteries?

While both capacitors and batteries store electrical energy, they do so in different ways. Capacitors store energy in an electric field, while batteries store energy through chemical reactions. Capacitors can also release their stored energy quickly, while batteries release it slowly over time.

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