Energy Stored In A Capacitor (Copy)

Understanding Energy Storage in Capacitors

• A capacitor stores electrical potential energy when it is charged.
• This energy is stored in the electric field between the plates due to the separation of positive and negative charges.
• The energy stored can be represented by the area under a charge (Q) vs voltage (V) graph, which forms a right-angled triangle.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Energy from Q–V Graph

• The graph of charge (Q) versus voltage (V) for a capacitor is a straight line through the origin because:

  Q = CV

• The area under the Q–V graph represents the energy (W) stored in the capacitor.
• This area is a triangle with:
  • Base = Q
  • Height = V
• So:

  W = ½ × Q × V = ½QV

Energy Stored – Different Formulas

• From the basic equation:

  W = ½QV

• Using Q = CV, we can substitute to get two alternate forms:
  • W = ½CV²
  • W = Q²/(2C)
• Therefore, the three equivalent forms of the energy stored in a capacitor are:
  

  Formula	Variables Involved
  W = ½QV	Charge and potential difference
  W = ½CV²	Capacitance and potential difference
  W = Q²/(2C)	Charge and capacitance

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Units of Energy

• The SI unit of energy is the joule (J)
• Energy stored is always positive, regardless of whether the capacitor is charging or discharging

Energy Stored During Charging

• As the capacitor charges:
  • Charge increases from 0 to Q
  • Voltage increases from 0 to V
  • Work must be done against the electric field to move charges onto the plates
• This work is stored as potential energy

Energy Transfer During Discharge

• When the capacitor is discharged through a resistor:
  • Stored energy is converted into thermal energy (heat) in the resistor
  • Not all energy is used for useful work unless a controlled discharge is used (e.g. in circuits)

Summary Table

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Graphical Understanding

• The Q–V graph is a straight line:
  • Q on y-axis, V on x-axis
  • Area under graph = ½QV = energy stored
• The V–t graph and Q–t graph during charging/discharging are exponential, not linear

Worked Example

Q: A 200 µF capacitor is charged to 12 V. How much energy is stored?

Solution:

• C = 200 × 10⁻⁶ F
• V = 12 V

W = ½CV²
W = ½ × 200 × 10⁻⁶ × 12² = ½ × 200 × 144 × 10⁻⁶ = 14.4 × 10⁻³ J = 0.0144 J

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course