Energy stored in combination of Capacitors

Energy stored in combination of Capacitors equals the sum of the energies stored in individual capacitors. Let’s see how we can show this mathematically using equations.

To find out the Energy stored in combination of Capacitors, we need to find out the equivalent capacitance (C_eq) and use this value in the equation of stored energy.

Energy stored in series combination of Capacitors

In series combination same charge (Q) builds up in all the capacitors in series.

Here, we will use this equation to express the energy stored in series combination of Capacitors: U_total = (1/2) Q²/C_eq

[ here C_eq is the equivalent capacitance of series combination of capacitors ]

=> U_total = (1/2) Q²(1/C_eq)

=>U_total = (1/2) Q² (1/C₁ + 1/C₂ + 1/C₃ + –)

=> U_total = (1/2) Q²/C₁ + (1/2) Q²/C₂ + (1/2) Q²/C₃ + —

=> U_total = U₁ + U₂ + U₃ + —

This means, Energy stored in series combination of Capacitors equals the sum of the energies stored in individual capacitors in series.

Energy stored in parallel combination of Capacitors

In parallel combination same potential difference (V) is applied across all the capacitors in parallel.

Here, we will use this equation to express the energy stored in series combination of Capacitors: U_total = (1/2) C_eq V²

[ here C_eq is the equivalent capacitance of parallel combination of capacitors ]

=> U_total =(1/2) C_eq V²

=>U_total = (1/2) (C₁ + C₂ + C₃ + –) V²

=> U_total = (1/2) C₁V² + (1/2) C₂V² + (1/2) C₃V² + —

=> U_total = U₁ + U₂ + U₃ + —

This means, Energy stored in parallel combination of Capacitors equals the sum of the energies stored in individual capacitors in parallel.