RESISTANCE OF HUMAN BODY BASIC INFORMATION AND TUTORIALS

For dc and 50 Hz or 60 Hz ac currents, the human body can be approximated by a resistance. The current path typically considered is from one hand to both feet, or from one foot to the other one.

The internal resistance of the body is approximately 300 Ω, whereas values of body resistance including skin range from 500 Ω to 3000 Ω, as suggested in Daziel, Geddes and Baker , Gieiges, Kiselev [B94], and Osypka [B118].

The human body resistance is decreased by damage or puncture of the skin at the point of contact. Conducted extensive tests using saltwater to wet hands and feet to determine safe let-go currents, with hands and feet wet.

Values obtained using 60 Hz for men were as follows: the current was 9.0 mA; corresponding voltages were 21.0 V for hand-to-hand and 10.2 V for hand-to-feet.

Hence, the ac resistance for a hand-to-hand contact is equal to 21.0/0.009 or 2330 Ω, and the hand-to feet resistance equals 10.2/0.009 or 1130 Ω, based on this experiment.

Thus, for the purposes of this guide, the following resistances, in series with the body resistance, are assumed as follows:

a) Hand and foot contact resistances are equal to zero.

b) Glove and shoe resistances are equal to zero.

A value of 1000 Ω in Equation (10), which represents the resistance of a human body from hand-to-feet and also from hand-to-hand, or from one foot to the other foot, will be used throughout this guide. RB = 1000 Ω

TEMPERATURE COEFFICIENT OF ELECTRICAL RESISTANCE BASIC AND TUTORIALS

The resistance for most resistors changes with temperature. The temperature coefficient of electrical resistance is the change in electrical resistance of a resistor per unit change in temperature.

The temperature coefficient of resistance is measured in W/°C. The temperature coefficient of resistors may be either positive or negative.

A positive temperature coefficient denotes a rise in resistance with a rise in temperature; a negative temperature coefficient of resistance denotes a decrease in resistance with a rise in temperature.

Pure metals typically have a positive temperature coefficient of resistance, while some metal alloys such as constantin and manganin have a zero temperature coefficient of resistance.

Carbon and graphite mixed with binders usually exhibit negative temperature coefficients, although certain choices of binders and process variations may yield positive temperature coefficients. The temperature coefficient of resistance is given by


R(T2) =R(T1)[1 +aT1(T2–T1)]


where aT1is the temperature coefficient of electrical resistance at reference temperature T1, R (T2) is the resistance at temperature T2(W), and R(T1) is the resistance at temperature T1(W).

The reference temperature is usuallytaken to be 20°C. Because the variation in resistance between any two temperatures is usually not linear as predicted by Eq, common practice is to apply the equation between temperature increments and then to plot the resistance change versus temperature for a number of incremental temperatures.

VARIABLE RESISTORS DEFINITION BASIC AND TUTORIALS

Potentiometers. The potentiometer is a special form of variable resistor with three terminals. Two terminals are connected to the opposite sides of the resistive element, and the third connects to a sliding contact that can be adjusted as a voltage divider.

Potentiometers are usually circular in form with the movable contact attached to a shaft that rotates. Potentiometers are manufactured as carbon composition, metallic film, and wire-wound resistors available in single-turn or multiturn units.

The movable contact does not go all the way toward the end of the resistive element, and a small resistance called the hop-off resistance is present to prevent accidental burning of the resistive element.

Rheostat. The rheostat is a current-setting device in which one terminal is connected to the resistive element and the second terminal is connected to a movable contact to place a selected section of the resistive element into the circuit.

Typically, rheostats are wire-wound resistors used as speed controls for motors, ovens, and heater controls and in applications where adjustments on the voltage and current levels are required, such as voltage dividers and bleeder circuits.

FIXED RESISTORS DEFINITION BASIC AND TUTORIALS

The fixed resistors are those whose value cannot be varied after manufacture. Fixed resistors are classified into composition resistors, wire-wound resistors, and metal-film resistors. Table 1.2 outlines the characteristics of some typical fixed resistors.


TABLE 1.2 Characteristics of Typical Fixed Resistors
Operating
Resistor Types Resistance Range Watt Range Temp. Range a, ppm/°C
Wire-wound resistor
Precision 0.1 to 1.2 MW 1/8 to 1/4 –55 to 145 10
Power 0.1 to 180 kW 1 to 210 –55 to 275 260
Metal-film resistor
Precision 1 to 250 MW 1/20 to 1 –55 to 125 50–100
Power 5 to 100 kW 1 to 5 –55 to 155 20–100
Composition resistor
General purpose 2.7 to 100 MW 1/8 to 2 –55 to 130 1500



Wire-Wound Resistors. Wire-wound resistors are made by winding wire of nickel-chromium alloy on a ceramic tube covering with a vitreous coating. The spiral winding has inductive and capacitive characteristics that make it unsuitable for operation above 50 kHz. The frequency limit can be raised by noninductive winding so that the magnetic fields produced by the two parts of the winding cancel.

Composition Resistors. Composition resistors are composed of carbon particles mixed with a binder. This mixture is molded into a cylindrical shape and hardened by baking.

Leads are attached axially to each end, and the assembly is encapsulated in a protective encapsulation coating. Color bands on the outer surface indicate the resistance value and tolerance. Composition resistors are economical and exhibit low noise levels for resistances above 1 MW.

Composition resistors are usually rated for temperatures in the neighborhood of 70°C for power ranging from 1/8 to 2 W. Composition resistors have end-to-end shunted capacitance that may be noticed at frequencies in the neighborhood of 100 kHz, especially for resistance values above 0.3 MW.

Metal-Film Resistors. Metal-film resistors are commonly made of nichrome, tin-oxide, or tantalum nitride, either hermetically sealed or using molded-phenolic cases. Metal-film resistors are not as stable as the wire wound resistors.

Depending on the application, fixed resistors are manufactured as precision resistors, semiprecision resistors, standard general-purpose resistors, or power resistors. Precision resistors have low voltage and power coefficients, excellent temperature and time stabilities, low noise, and very low reactance.

These resistors are available in metal-film or wire constructions and are typically designed for circuits having very close resistance tolerances on values. Semiprecision resistors are smaller than precision resistors and are primarily used for current-limiting or voltage-dropping functions in circuit applications. Semiprecision resistors have long-term temperature stability.

General-purpose resistors are used in circuits that do not require tight resistance tolerances or long-term stability. For general-purpose resistors, initial resistance variation may be in the neighborhood of 5% and the variation in resistance under full-rated power may approach 20%.

Typically, general-purpose resistors have a high coefficient of resistance and high noise levels. Power resistors are used for power supplies, control circuits, and voltage dividers where operational stability of 5% is acceptable. Power resistors are available in wire-wound and film constructions. Film-type power resistors have the advantage of stability at high frequencies and have higher resistance values than wire-wound resistors for a given size.

WHAT IS RESISTANCE (CIRCUIT ANALYSIS) – DEFINITION BASICS AND TUTORIALS

To say that Ohm’s law is true for a particular conductor is to say that the resistance of this conductor is, in fact, constant with respect to current and voltage. Certain materials and electronic devices exhibit a nonlinear relationship between current and voltage, that is, their resistance varies depending on the voltage applied.

The relationship V = IR will still hold at any given time, but the value of R will be a different one for different values of V and I. These nonlinear devices have specialized applications and will not be discussed in this chapter.

Resistance also tends to vary with temperature, though a conductor can still obey Ohm’s law at any one temperature. For example, the resistance of a copper wire increases as it heats up. In most operating regimes, these variations are negligible.

Generally, in any situation where changes in resistance are significant, this is explicitly mentioned. Thus, whenever one encounters the term “resistance” without further elaboration, it is safe to assume that within the given context, this resistance is a fixed, unchanging property of the object in question.

Resistance depends on an object’s material composition as well as its shape. For a wire, resistance increases with length, and decreases with cross-sectional area. Again, the analogy to a gas or water pipe is handy: we know that a pipe will allow a higher flow rate for the same pressure difference if it has a greater diameter, while the flow rate will decrease with the length of the pipe.

This is due to friction in the pipe, and in fact, an analogous “friction” occurs when an electric current travels through a material.

This friction can be explained by referring to the microscopic movement of electrons or ions, and noting that they interact or collide with other particles in the material as they go. The resulting forces tend to impede the movement of the charge carriers and in effect limit the rate at which they pass.

These forces vary for different materials because of the different spatial arrangements of electrons and nuclei, and they determine the material’s ability to conduct. This intrinsic material property, independent of size or shape, is called resistivity and is denoted by r (the Greek lowercase rho).

The actual resistance of an object is given by the resistivity multiplied by the length of the object (l ) and divided by its cross-sectional area (A): R = RHO X LENGTH/ AREA

The units of resistance are ohms, (Greek capital omega). By rearranging Ohm’s law, we see that resistance equals voltage divided by current. Units of resistance are thus equivalent to units of voltage divided by units of current. By definition, one ohm equals one volt per ampere (OHM = V/A).

The units of resistivity are ohm-meters (OHM-m), which can be reconstructed through the preceding formula: when ohm-meters are multiplied by meters (for l ) and divided by square meters, the result is simply ohms.

Resistivity, which is an intrinsic property of a material, is not to be confused with the resistance per unit length (usually of a wire), quoted in units of ohms per meter (oHM/m). The latter measure already takes into account the wire diameter; it represents, in effect, the quantity rho/A. The resistivities of different materials in V-m can be found in engineering tables.

RESISTANCE IN PARALLEL BASIC INFORMATION AND TUTORIALS

What Happens To Resistance When Connected In Parallel?

When resistors are combined in parallel, the effect is perhaps less obvious than for the series case: rather than adding resistance, we are in fact decreasing the overall resistance of the combination by providing alternative paths for the current.

This is so because in the parallel case the individual charge is not required to travel through every element, only one branch, so that the presence of the parallel elements “alleviates” the current flow through each branch, and thereby makes it easier for the charge to traverse.

It is convenient here to consider resistors in terms of the inverse property, conductance. Thus, we think of the resistor added in parallel not as posing a further obstacle, but rather as providing an additional conducting option: after all, as far as the current is concerned, any resistor is still better than no path at all. Accordingly, the total resistance of a parallel combination will always be less than any of the individual resistances.


Using conductance (G = 1/R), the algebraic rule for combining any number of resistive elements in parallel is simply that the conductance of the parallel combination equals the sum of the individual conductances.

For example, suppose a 10-ohm and a 2.5-ohm resistor are connected in parallel, as in figure below.

We know already that their combined (parallel) resistance must be less than 2.5 ohm. To do the math, it is convenient to first write each in terms of conductance: 0.1 mho and 0.4 mho. The combined conductance is then simply the sum of the two, 0.5 mho. Expressed in terms of resistance, this result equals 2 ohm. In equation form, we would write for resistors in parallel:

1/Rt = 1/R1 + 1/R2 + ....


Note that the voltage drop across any number of elements in parallel is the same. This can easily be seen because all the elements share the same terminals: the points where they connect to the rest of the circuit are, in electrical terms, the same.

While elements connected in parallel thus have a common voltage drop across them, the current flowing through the various elements or branches will typically differ. Intuitively, we might guess that more current will flow through a branch with a lower resistance, and less current through one with a higher resistance.

This can be shown rigorously by applying Ohm’s law for each of the parallel resistances: If V is the voltage drop common to all the parallel resistances, and R1 is the individual resistance of one branch, then the current I1 through this branch is given by V/R1. Thus, the amount of current through each branch is inversely proportional to its resistance.

To summarize, there is a tidy correspondence between the series and parallel cases: In a series connection, the current through the various elements is the same, but the voltage drops across them vary (proportional to their resistance); in a parallel connection, the voltage drop across the various elements is the same, but the currents through them vary (inversely proportional to their resistance).

RESISTANCE IN SERIES BASIC INFORMATION AND TUTORIALS

What Happens To Resistance In Series?


The simplest kind of combination of multiple circuit elements has resistors connected in series (figure below).

The rule is easy: to find the resistance of a series combination of resistors, add their individual resistances.

For example, if a 10-ohm resistor is connected in series with a 20-ohm resistor, their combined resistance is 30 ohm. This means that we could replace the two resistors with a single resistor of 30 ohm and make no difference whatsoever to the rest of the circuit.

In fact, if the series resistors were enclosed in a box with only the terminal ends sticking out, there would be no way for us to tell by electrical testing on the terminals whether the box contained a single 30-ohm resistor or any series combination of two or more resistors whose resistances added up to 30 ohm.

Thus, an arbitrary number of resistances can be added in series, and their order does not matter.

Intuitively, the addition rule makes sense because if we think of a resistor as posing an “obstacle” to the current, and note that the same current must travel through each element in the series, each obstacle adds to the previous ones.

This notion can be formalized in terms of voltage drop. Across each resistor in a series combination, there will be a voltage drop proportional to its resistance. It is always true that, regardless of the nature of the elements (whether they are resistors or something else), the voltage drop across a set of elements connected in series equals the sum of voltage drops across the individual elements.

This notion reappears in the context of Kirchhoff’s Voltage Law.