LEARNING OBJECTIVES
- Explain how energy is stored in a capacitor
- Use energy relations to determine the energy stored in a capacitor network
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
Strategy
We use Equation 4.3.2 to find the energy
Solution
We identify
The total energy stored in this network is
Significance
We can verify this result by calculating the energy stored in the single
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.
Candela Citations
CC licensed content, Specific attribution
- Download for free at //cnx.org/contents/. Retrieved from: //cnx.org/contents/. License: CC BY: Attribution