What is energy stored in a capacitor?

Short Answer

The energy stored in a capacitor is the electrical energy kept inside it due to the separation of charges on its two plates. When a capacitor is connected to a voltage source, one plate becomes positively charged and the other becomes negatively charged. The work done to move these charges gets stored as energy in the electric field between the plates.

This stored energy can be released whenever needed, such as in camera flashes, power backup systems, and electronic circuits. The amount of energy stored depends on the capacitance of the capacitor and the voltage applied across it.

Detailed Explanation

Energy stored in a capacitor

The energy stored in a capacitor is the electrical energy accumulated in the electric field between its plates. A capacitor is a device that stores electric charge by holding opposite charges on two metal plates separated by a dielectric. When a voltage source such as a battery is connected to the capacitor, charges begin to accumulate:

  • The plate connected to the positive terminal becomes positively charged.
  • The plate connected to the negative terminal becomes negatively charged.

This separation of charges creates an electric field between the plates. The work done by the voltage source to separate the charges is not lost; it gets stored in the form of electrostatic potential energy. This stored energy can be used later in the circuit whenever required.

Why energy is stored

When electrons move from one plate to another under the influence of the voltage source, work must be done to move each additional electron because the charge on the plates increases. Moving charges against an electric force requires work, and this work becomes stored as potential energy.

The more charge a capacitor stores, the more energy it holds. The energy is stored only as long as the charges remain separated. Once the capacitor discharges by providing current to a circuit, the stored energy is released.

Formula for energy stored

The energy stored in a capacitor is given by:

U = 1/2 C V²

Where,

  • U is the energy stored in joules (J),
  • C is the capacitance in farads (F),
  • V is the potential difference across the capacitor in volts (V).

This formula shows:

  • Energy increases when capacitance increases.
  • Energy increases more rapidly when voltage increases because voltage is squared.

Derivation of the formula (simple explanation)

The work done to move a small amount of charge dq to the capacitor against the electric field is:

dW = V dq

But initially, the voltage across the capacitor is zero, and it increases as more charge is added.
The voltage at any moment is:

V = q / C

Substituting this:

dW = (q / C) dq

When we integrate this from 0 to Q (total charge), we get:

W = 1/2 (Q² / C)

Using the relation Q = CV, the formula becomes:

U = 1/2 C V²

This shows how the capacitor stores energy in its electric field.

Where the energy is stored

The energy in a capacitor is stored in the electric field between the plates. This field is created by the separation of charges. The dielectric material between the plates also plays a role in storing energy by reducing the electric field and allowing more charge to accumulate.

Factors affecting stored energy

The energy stored in a capacitor depends on:

  1. Capacitance (C):
    Higher capacitance means more charge can be stored, leading to more energy.
  2. Voltage (V):
    Higher voltage stores much more energy because energy depends on V².
  3. Dielectric material:
    A dielectric with a high dielectric constant increases capacitance, which increases stored energy.
  4. Plate area and distance:
    Large plate area and small distance between plates increase capacitance and energy storage.

Examples of energy stored in capacitors

Capacitors store energy in many useful ways:

  1. Camera flash:
    A capacitor stores energy and releases it quickly to produce a bright flash.
  2. Power supplies:
    Capacitors smooth the voltage by storing and releasing energy whenever needed.
  3. Electric vehicles:
    Supercapacitors store large amounts of energy for quick acceleration.
  4. Mobile phones and laptops:
    Capacitors regulate power and keep circuits stable.
  5. Motors and fans:
    Capacitors help start motors by providing stored energy for an extra push.

Charging and discharging

During charging, energy is stored in the electric field between the plates.
During discharging, the stored energy is released and used to do work in the circuit.

The speed of charging and discharging depends on resistance in the circuit. This process is used in timing devices, alarms, and signal processors.

Limit to stored energy

Every capacitor has a maximum voltage it can handle. If too much voltage is applied:

  • The dielectric may break down.
  • The capacitor may get damaged.
  • Stored energy may release suddenly.

Thus, capacitors must be used within their rated voltage limits.

Conclusion

The energy stored in a capacitor is the electrostatic potential energy created by the separation of charges on its plates. This energy depends on capacitance and voltage and is stored in the electric field between the plates. Capacitors use this stored energy to power circuits, smooth voltage, start motors, and perform many essential functions in electronic devices. Understanding this energy is important for studying capacitors and modern electrical applications.