What is a component that has an ability to store electrical energy in an electric field?

LEARNING OBJECTIVES

Most of us have seen dramatizations of medical personnel using a defibrillator to pass an electrical current through a patient’s heart to get it to beat normally. Often realistic in detail, the person applying the shock directs another person to “make it

(Figure 4.3.1)  

Figure 4.3.1 The capacitors on the circuit board for an electronic device follow a labeling convention that identifies each one with a code that begins with the letter “C.”

The energy

To gain insight into how this energy may be expressed (in terms of

(4.3.1)  

If we multiply the energy density by the volume between the plates, we obtain the amount of energy stored between the plates of a parallel-plate capacitor:

In this derivation, we used the fact that the electrical field between the plates is uniform so that

(4.3.2)  

The expression in Equation 4.3.1 for the energy stored in a parallel-plate capacitor is generally valid for all types of capacitors. To see this, consider any uncharged capacitor (not necessarily a parallel-plate type). At some instant, we connect it across a battery, giving it a potential difference

This work becomes the energy stored in the electrical field of the capacitor. In order to charge the capacitor to a charge

Since the geometry of the capacitor has not been specified, this equation holds for any type of capacitor. The total work

Knowing that the energy stored in a capacitor is

We see that this expression for the density of energy stored in a parallel-plate capacitor is in accordance with the general relation expressed in Equation 4.3.1. We could repeat this calculation for either a spherical capacitor or a cylindrical capacitor—or other capacitors—and in all cases, we would end up with the general relation given by Equation 4.3.1.

EXAMPLE 4.3.1

Energy Stored in a Capacitor

Calculate the energy stored in the capacitor network in Figure 4.2.4(a) when the capacitors are fully charged and when the capacitances are

, 

, and 

 respectively.

Strategy

We use Equation 4.3.2 to find the energy

,

, and

 stored in capacitors

,

, and

, respectively. The total energy is the sum of all these energies.

Solution

We identify 

 and

, 

 and

, 

 and

. The energies stored in these capacitors are

   

The total energy stored in this network is

   

Significance

We can verify this result by calculating the energy stored in the single 

 capacitor, which is found to be equivalent to the entire network. The voltage across the network is

. The total energy obtained in this way agrees with our previously obtained result,

.

CHECK YOUR UNDERSTANDING 4.6

In a cardiac emergency, a portable electronic device known as an automated external defibrillator (AED) can be a lifesaver. A defibrillator (Figure 4.3.2) delivers a large charge in a short burst, or a shock, to a person’s heart to correct abnormal heart rhythm (an arrhythmia). A heart attack can arise from the onset of fast, irregular beating of the heart—called cardiac or ventricular fibrillation. Applying a large shock of electrical energy can terminate the arrhythmia and allow the body’s natural pacemaker to resume its normal rhythm. Today, it is common for ambulances to carry AEDs. AEDs are also found in many public places. These are designed to be used by lay persons. The device automatically diagnoses the patient’s heart rhythm and then applies the shock with appropriate energy and waveform. CPR (cardiopulmonary resuscitation) is recommended in many cases before using a defibrillator.

(Figure 4.3.2)  

Figure 4.3.2 Automated external defibrillators are found in many public places. These portable units provide verbal instructions for use in the important first few minutes for a person suffering a cardiac attack.