Energy in Capacitor

Defibrillator

A medical device that passes an electrical current through a patient’s heart to restore a normal heartbeat, using the energy stored in a capacitor.

Capacitor in Defibrillator

Stores electrical energy that can be released as a controlled shock to the heart with an adjustable energy levels such as 400 joules.

Joules

The SI unit of energy, used to measure the amount of electrical energy delivered by devices like defibrillators

Capacitors in microelectronics

Provide temporary energy storage in small devices, such as supplying power when batteries are charged.

Capacitors in cameras

Store and release energy to power flash lamps in cameras, enabling bright flashes of light for photography.

Energy storage in capacitor

A charged capacitor stores energy in the electric field between its plates

Charging process of capacitor

As capacitor is charged, the electric field between its plates builds up gradually

Capacitor after disconnection

When a charged capacitor is disconnected from a battery, it’s stored energy remains in the electrical field between the plates.

Ad

Formula to find the volume of the space between a capacitor’s plates

uniform electrostatic field

The space between a capacitor’s plates is filled with a ___________________________ where the energy stored is contained.

Uc

Symbol that represents the total energy of the capacitor

Energy density (Ue)

Defined as Uc/Ad

Uc = Ue(Ad)

Formula to find the total energy stored in a capacitor if we know the value of the energy density

Yes, it is true

Is it true that the energy density (Ue) in a region of free space occupied by an Electrical field depends only on the magnitude of the field?

Ue = (1/2)*ε0*E^2

Formula to find the energy density in a region of the free space occupied by an electrical field.

E = V/d

Formula for the Electrical field

Uc = (1/2)*ε0*E^2*A*d

TOTAL energy in the capacitor expressed in term of the Electrical field.

Uc = (1/2)*ε0*(V^2/d^2)*A*d

Substituting the definition of the Electrical field inside the “Total energy stored inside the capacitor formula in terms of the Electrical field”

Uc = (1/2)*(V^2)*ε0*A/d

Simplifying the formula of the Total energy of the capacitor inside which devotion of the electrical field was substituted.

C = ε0(A/d)

Formula to calculate the capacitance of the parallel plate capacitor

Uc = (1/2)*(V^2)*C

Final form of the formula to calculate the total energy inside the parallel plate capacitor.

Uc = (1/2)*(Q^2/C)

Second form of the formula to find the total energy in capacitor (Used when we are not given the voltage)

Also, the final form of the integration equation to find the total work done in capacitor to charge the capacitor to a certain charge of Q.

Uc = (1/2)*Q*V

Third form of the formula to find the total energy stored inside the capacitor. (Used when we are not given the capacitance)

V = Q/C

Formula to find the voltage between the capacitor plates when we know the charge and capacitance.

dW = V dq = q/C dq

The derivational equation that defines the work required to move a tiny charge dq from the negative to the positive plate.

This is the work required to move an infinitesimal charge.

The work done on the charge in moving them from negative plate to the positive plate becomes the stored energy in the capacitor’s electrical field.

What is the relation of the work to the energy in the context of capacitors

W = ∫(from 0 to W(Q)) dW = ∫(from 0 to Q) (q/C)dq

The integration equation of the total work required to charge the capacitor to the charge of Q.

Uc = W

Mathematical form for “The total work W needed to charge a capacitor is the electrical potential energy Uc stored in it.

Ue = (1/2)*(Q^2/C)*(1/Ad)

Substituting the appropriate definition of the Uc inside the definition of Ue.

Ue = (1/2)*(Q^2/(ε0*(A/d)))*(1/Ad)

Substituting the definition of Capacitance of a parallel-plate capacitor inside the definition of Ue where the appropriate definition of Uc has already been substituted.

Ue = (1/2)*(1/ε0)*(Q/A)^2

Simplified equation of the C→Uc→Ue

E = σ/ε0

Formula to calculate the Electrical field inside the parallel plate capacitor.

Ue = (σ^2)/(2ε0)

Substituting the definition of the surface charge density in the Simplified equation of the C→Uc→Ue

Ue = ((Eε0)^2)/2ε0

Defining the surface charge density in terms of the Electrical field and the permittivity constant in the Simplified equation of the C→Uc→Ue

Ue = (ε0/2)*E^2

Final form of the E→σ→C→Uc→Ue Energy density equation.

Automated External Defibrillator (AED)

A portable electronic device that delivers a large charge in a short burst to correct the abnormal heart rhythms during cardiac emergencies.

Ventricular fibrillation

A severe type of arrhythmia where the heart’s ventricles (the lower chambers of the heart) shake rapidly and irregularly instead of pumping blood properly.

Purpose of the Defibrillator shock

A strong electrical shock can stop arrhythmia and allow the body’s natural pacemaker to restore the normal rhythm

AED usability

AEDs are designed in a way that even a layperson can use it safely; the device automatically diagnoses heart rhythm and applies the correct shock.

Shock adjustment

The AED automatically delivers shocks with appropriate energy and waveform based on the patient’s condition.

CPR

What is often recommended in many cases before using a defibrillator?

Cardiopulmonary Resuscitation

Full form of CPR