physicscatalyst.com logo




Energy stored in capacitor





7. Energy stored in a capacitor



  • Consider a capacitor of capacitance C, completely uncharged in the begning.
  • Charhing process of capacitor requires expanditure of energy because while charging a capacitor charge is transferred from plate at lower potential to plate at higher potential.
  • Now if we start charging capacitor by transporting a charge dQ from negative plate ti the positive plate then work is done against the potential difference across the plate.
  • If q is the amount of charge on the capacitor at any stage of charging process and φ is the potential difference across the plates of capacitor then magnitude of potential difference is φ=q/C.
  • Now work dW required to transfer dq is
    dW=φdq=qdq/C
  • To charge the capacitor starting from the uncharged state to some final charge Q work required is
    Integrating from 0 to Q
         W=(1/C)∫qdq
         =(Q2)/2C      
    (14a)
         =(CV2)/2
         =QV/2


    Which is the energy stored in the capacitor and can also be written as
         U=(CV2)/2 ---(15)

  • From equation 14c,we see that the total work done is equal to the average potential V/2 during the charging process ,multiplied by the total charge transferred
  • If C is measured in Farads ,Q in coulumbs and V in volts the energy stored would in Joules
  • A parallel plate capacitor of area A and seperation d has capacitance

    C=ε0A/d

  • electric field in the space between the plates is
    E=V/d or V=Ed

    Putting above values of V and C in equation 14b we find
    W=U=(1/2)(ε0A/d)(Ed)2
    =(1/2)ε0E2(Ad)
    =(1/2)ε0E2.V
    ---(16)

  • If u denotes the energy per unit volume or energy density then
    u=(1/2)ε0E2 x volume
  • The result for above equation is generally valid even for electrostatic field that is not constant in space.












Latest Updates
Classification of Elements JEE MCQ

Chemical Equilibrium Class 11 MCQ

Redox Reactions JEE Main MCQ

Chemical Equilibrium Class 11 MCQ

Chemical Thermodynamics JEE Advanced MCQ