How Does Charge Increase Affect Capacitor Energy and Potential Difference?

In summary, the correct answer is B) 2.25E and 1.5V. The potential difference increases by 50% when the charge is increased by 50%, and using the equation E = 0.5 CV^2, we can see that the energy increases by 2.25 times the original amount. It is also important to note that the capacitor's capacitance, C, remains constant in this scenario.
  • #1
v_pino
169
0

Homework Statement



A capacitor of capacitance C stores an amount of energy E when the pd across it is V. Which line, A to D, gives the correct energy and pd when the charge is increased by 50%?

Energy pd
A) 1.25E 1.5V
B) 2.25E 1.5V


Homework Equations



E= 0.5 CV^2
E= 0.5 QV

C= Q/V


The Attempt at a Solution



The answer is B).

Do I have to find two simultaneous equations because I have two unknowns? But how?

Thanks :)
 
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  • #2
You know that C doesn't change (it's the same capacitor) and you are told how Q changes. Use the last of your three equations to figure out what happens to the potential difference. Then use either of the other equations to see what happens to the energy.
 
  • #3
thanks! :D
 
  • #4
When charges increase by 50%

then by equation Q = C*V we can know that V increases by 50% so, it changes from V to 1.5V

then by using equation E = 1/2*C*V^2
then V is changed to 1.5V so, use that in the above equation (1.5)^2 = 2.25
hence it becomes 2.25E
 
  • #5
You are several days too late. :wink:
 
  • #6
Doc Al said:
You are several days too late. :wink:

Hi Doc Al - I just joined the forum & picked up a question that I first saw!

Isn't it appropriate?
 
  • #7
bhimsen said:
Isn't it appropriate?
Actually, no. :wink:
(1) You are more than welcome to chime in, but read the thread first before doing so. If you did you'd see that the OP had already solved the problem.
(2) Never just post full solutions to a problem. See our rules posted at the top of each page and the https://www.physicsforums.com/showthread.php?t=94379".

Nonetheless, welcome to PF! :smile:
 
Last edited by a moderator:

1. What is energy in a capacitor?

Energy in a capacitor refers to the stored electrical energy that is present between the two plates of the capacitor. This energy is in the form of an electric field and is created when the capacitor is charged with an external power source.

2. How is energy stored in a capacitor?

Energy is stored in a capacitor by the separation of charges on the two plates of the capacitor. When a capacitor is connected to a power source, the positive charges accumulate on one plate while the negative charges accumulate on the other plate, creating an electric field and storing energy.

3. What is the relationship between energy and capacitance?

The amount of energy stored in a capacitor is directly proportional to its capacitance. This means that a capacitor with a higher capacitance will be able to store more energy than a capacitor with a lower capacitance, given the same voltage.

4. How is the potential difference (pd) related to the energy in a capacitor?

The potential difference, or voltage, across a capacitor is directly related to the amount of energy stored in the capacitor. This means that the higher the pd, the more energy is stored in the capacitor. The relationship between pd and energy is represented by the equation E = 1/2CV^2, where C is the capacitance and V is the voltage.

5. How can the energy stored in a capacitor be calculated?

The energy stored in a capacitor can be calculated using the equation E = 1/2CV^2, where E is the energy in joules, C is the capacitance in farads, and V is the voltage in volts. Alternatively, the energy can also be calculated by multiplying the charge on the capacitor by the pd across it, which is represented by the equation E = QV, where Q is the charge in coulombs and V is the voltage in volts.

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