MEASUREMENT USING ELECTRICITY

Principles of Electricity

Most of our monitors and other anesthesiology apparatus use the basic principles of electricity and magnetism. Nearly all of our transducers use some form of electrical energy as their output, and the subsequent data processing and display are entirely electrical. We review some of the principles in this section by using examples from medical equipment.

Static Electricity

Electricity is a manifestation of a property called charge that is inherent in matter. The charge can be negative, positive, or neutral. Static electricity involves charges at rest: like charges repel one another, whereas opposite charges attract. What we usually mean by the word "electricity" involves the flow of charges, or the electrical current. Current flows in one direction in "direct-current" (DC) electronic devices and alternates back and forth in "alternating-current" (AC) devices.

The SI unit of charge is the coulomb, and the smallest quantum of charge is the charge of an electron, which is equal but opposite the charge of a proton. An electrostatic force is exerted between two charged objects and is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them:

F = k × q₁ × q₂ /r² —Coulomb's law (7)

This force is attractive when the charges are of opposite sign and repulsive when they are of the same sign. In a Nobel Prize-winning experiment, Robert Millikan determined the charge of an electron by suspending charged oil drops between two horizontal charged plates such that the electrostatic force balanced the gravitational force and the drops were held in midair ( Fig. 30-26 ). Approximately 20 years later, his son, Glen Allen Millikan, developed one of the earliest infrared ear oximeters, the forerunner of the pulse oximeter (see the section on the pulse oximeter).

Direct Current

Just as mechanical energy may be stored as potential energy, electrical energy can be stored as a potential difference. A common analogy is to compare electrical potential difference with water pressure ( Fig. 30-27 , see Table 30-2 ). The potential difference (V) between points A and B is defined as the work required to move a unit charge from A to B (see the discussion of the relationship of work and energy, earlier in this chapter). The SI unit of potential difference is the volt; hence, the term voltage is often used for potential difference. Charges can move easily through conductors, but they do not move well through insulators, also called dielectrics. If a potential (V) exists between A and B and these two points are connected by a conductor, charges will flow between them and produce a current (I).

The SI unit of current is the coulomb per second, called the ampere. If A and B are separated by an insulator, no current will flow until the potential difference becomes so great that a breakdown of the insulator occurs. For example, if A and B are separated by dry air, no current will flow until the potential difference reaches 3000 V/mm. At this potential gradient, air suddenly becomes a conductor, and a current flows in the form of a visible (and audible) spark. To generate a spark between two electrodes 1 cm apart, one must create a potential difference of 30,000 V. Lightning is a larger manifestation of the same phenomenon.

A battery is a chemical cell that produces a constant potential difference between two electrodes, which is called electromotive force (EMF). The battery can provide a continuous source of electrons, or current, to flow through

Figure 30-26 Electric force. The quantity of charge on an electron was determined by balancing the electric force on an oil drop against the gravitational force on the same drop. F₁ = kq₁ q₂ /r² = F₂ = m₁ a_g .

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Figure 30-27 Water and electricity. The pressure drop over the dam (A to B) is analogous to the voltage drop over the resistance (A to B) (e.g., light bulb). The amount of flow (width of water) () is analogous to the current (I). Both falling water and electrical potential can do work, as evidenced by the use of dams to generate electricity and electricity to pump water.

This relationship is called Ohm's law, and materials that follow this behavior are called ohmic materials. This example is analogous to hemodynamic flow, in which the pressure drop (mean arterial pressure — central venous pressure) equals cardiac output times systemic vascular resistance.

ΔP = CO × SVR (9)

The power (i.e., rate of work, see discussion earlier in this chapter) required to drive an electric current is the product of voltage and current: P = VI. By combining this formula with Ohm's law (V = IR), we have P = I² R = V² /R. Thus, if we double the current through a fixed resistance (R), we use four times the original power. This power loss in resistors is dissipated as heat, which is the reason why nearly all electrical devices become warm during use.

A capacitor is a device that stores charge (Q) in direct proportion to the potential difference (V) between its two electrodes: Q = CV. The proportionality constant (C) is called capacitance, which is measured in SI units of farads. When a capacitor is connected to a battery, current flows until the capacitor is charged to the point that the potential across the capacitor equals the EMF of the battery: V = Q/C = EMF ( Fig. 30-28 ). When we push the "charge" button of a defibrillator, this kind of circuit is activated to charge a capacitor to the desired level. As shown in Figure 30-28B , time is required to charge a capacitor.

Figure 30-28 Resistance and capacitance in a direct-current circuit. A, Under direct current, the resistance impedes flow, with a voltage drop developing across the resistance. The capacitor allows current to flow until the charge builds on the capacitor (B). Under direct current, the voltage is constant over time, and the current flow decreases as the charge on the capacitor increases. This type of circuit is used to charge a defibrillator.

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Alternating Current

In an AC circuit, the current and the voltage fluctuate rapidly ( Fig. 30-29 ). There are many important differences between AC and DC power. The voltage in common AC house power fluctuates sinusoidally at a frequency of 60 Hz (50 Hz in Europe). We characterize the amplitude of such a fluctuating voltage by calculating its root mean square (RMS), that is, the square root of the time average of V² . Thus, for AC house power, V_RMS = 115 V (230 V in Europe). Current in an AC system is also constantly changing and is likewise measured as an RMS value.

AC circuits have three forms of impedance: resistance (R), capacitance (C), and inductance (L). An inductor is a circuit element whose impedance increases with the frequency (f) of the current fluctuations (R = 2πifL). Conversely, the impedance of a capacitor decreases with increasing frequency (R = ½πifC). Inductors thus tend to block high frequencies, whereas capacitors tend to block low frequencies ( Fig. 30-30 ). This principle is used in stereo systems to direct the signal to either the woofer (low-frequency) speaker or the tweeter (high-frequency) speaker. In medical

Figure 30-29 Resistance and capacitance in an alternating-current (AC) circuit. In an AC circuit (A), unlike a direct-current circuit, the capacitor does not block current flow. The capacitor and resistance act to shift the phase of the AC current. Current changes lag behind voltage changes (B).

Figure 30-30 Woofer and tweeter. Stereo speakers use resistors to act as impedance to the high-frequency components of sound, and only the bass frequencies are allowed to pass to the woofer speaker. Capacitors are used as a high-pass filter to allow only the high frequencies to get to the tweeter. The 60-Hz interference from electrical appliances can be decreased by a similar process. (From Hecht E: Physics: Algebra/Trig. Pacific Grove, CA, Brooks/Cole, 1994.)