Energy Stored in a Capacitor: Definition, Derivation, Formula & Class 12 Notes

Energy stored in a capacitor is defined as the amount of work done by the applied voltage to move the electron from one plate to the other against the electric field. The energy is stored in the form of an electric field between the plates.

A capacitor is an electronic component consisting of two conductive plates separated by an insulating material called a dielectric. When the current is applied to the capacitor, it moves the electrons from one plate to the other. The work done to move the electrons between the plates is stored as electrical potential energy. When the capacitor gets discharged, the stored energy is released. 

Formula for Stored Energy in a Capacitor: 

$U=\frac{1}{2}C{V}^2=\frac{Q^2}{2C}=\frac{1}{2}QV$

Where,

• C is capacitance
• U is energy stored
• V is the voltage across the capacitor
• Q charge on a capacitor

Energy stored in the capacitor is given as:

$u=\frac{1}{2}\epsilon E^2$

• Capacitance (parallel plate capacitor):  $C=\frac{\epsilon A}{d}$
• Electric Field: $E=\frac{V}{d}\Rightarrow V=Ed$
• Substituting energy: 

$U=\frac{1}{2}·\frac{\epsilon A}{d}·{\left(Ed\right)}^2=\frac{1}{2}\epsilon E^2·\left(Ad\right)$

Volume (between plates): A ⋅ d

Energy density in the electric field: 

$u=\frac{U}{\text{Volume}}=\frac{1}{2}\epsilon E^2$

Energy stored per unit volume in the space where the electric field exists is known as energy density in an electric field.

Energy density u of an electric field is given as:

$u=\frac{1}{2}\epsilon E^2$

Where, 

• $u$ represent the energy density (in J/m³) 
• ε is the permittivity of the medium between the plates (for vacuum, $\varepsilon = \varepsilon_0$)
• E is the electric field (in V/m)

Here we have provided the link for NCERT Class 12 Physics notes. The notes are available for all chapters.

Here is the link for the complete NCERT solution for Class 12 Physics.