Scaling factor of Energy in a capacitor with change in charge

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SUMMARY

The discussion centers on the scaling factor of energy in a capacitor when charge changes, specifically referencing AQA Section A Q18 from June 2011. The key equations involved are E = 0.5QV and C = Q/V. It is established that if the charge (Q) increases by 1.5 times while capacitance (C) remains constant, the voltage (V) must also increase by 1.5 times, resulting in the energy (E) increasing by a factor of 2.25. The logic and method applied in the solution are confirmed as correct by participants in the discussion.

PREREQUISITES
  • Understanding of capacitor fundamentals, including charge (Q), voltage (V), and capacitance (C).
  • Familiarity with the energy storage formula for capacitors: E = 0.5QV.
  • Knowledge of the relationship between charge, voltage, and capacitance: C = Q/V.
  • Basic algebra skills to manipulate equations and understand scaling factors.
NEXT STEPS
  • Study the derivation and implications of the energy formula E = 0.5CV².
  • Explore the effects of varying capacitance on energy storage in capacitors.
  • Investigate real-world applications of capacitors in electrical circuits.
  • Learn about the impact of dielectric materials on capacitance and energy storage.
USEFUL FOR

Students studying electrical engineering, physics enthusiasts, and educators looking to deepen their understanding of capacitor behavior and energy storage principles.

mrcotton
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Homework Statement


AQA Section A Q18 Jun 11
photbucket3_zps580de911.jpg


Homework Equations



The answer should be C

E=.5QV and C=Q/V

The Attempt at a Solution



So the original Q has increased by 1.5 times If C is constant than the voltage must also increase by 1.5 times

Now the energy E is E=.5QV V has increase by 1.5 and and so has Q which is 2.25

Infact in typing this out I think I just solved it. Is this logic and method ok
 
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mrcotton said:

Homework Statement


AQA Section A Q18 Jun 11
photbucket3_zps580de911.jpg


Homework Equations



The answer should be C

E=.5QV and C=Q/V

The Attempt at a Solution



So the original Q has increased by 1.5 times If C is constant than the voltage must also increase by 1.5 times

Now the energy E is E=.5QV V has increase by 1.5 and and so has Q which is 2.25

Infact in typing this out I think I just solved it. Is this logic and method ok

Seems fine to me.
 
Yup. You may recall that the energy stored in a capacitor is also given by:


[itex]E = \frac{1}{2}CV^2[/itex]
 

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