18 Circuit Components

Vinay Gupta

   Circuit Components (Resistors, Inductors and Capacitors)

It is almost impossible to manufacture a component so that it has only one property. For example, a resistor has an associated inductance and capacitance, a capacitor has leakage resistance and an inductor has resistance and interturn capacitance. The impurities present in a component produce unwanted quantities which are called Residues. However, a particular quantity like resistance in a resistor, capacitance in a capacitor, inductance in an inductor may be made to dominate and so that the effect of residues is very small and it is possible to design pure components for specified limits of accuracy.

Resistors

Resistive networks and Resistors are extensively used in instrumentation systems and for measurement work. Resistors must satisfy some extremely important properties for precision measurement work such as: they must be stable or show permanence with time as it is required to avoid the change in value of resistance with time. They must have robust construction and small temperature co-efficient. It is required in order that the variation in resistance values owing to change in temperature is small. They should have low thermoelectric e.m.f. with copper. The thermoelectric emf with copper is particularly important in bridge networks and potentiometers, as large measuring errors may occur even if the thermoelectric emf is a few eV. They should have high resistivity. It is required in order that the size of the resistors is small. The resistor material should show resistance to oxidation, corrosion and moisture. Also, they should have ease in manufacture and should be cheap.

Materials suitable for use as Resistors:

A single material cannot possess all the above mentioned properties and, hence, only that material is selected which is best suited for the particular case. The most widely used materials for precision resistors are:

Manganin: It is an alloy of copper, manganese and nickel and is universally used as resistance material for precision resistors and for resistance measuring apparatus. It has a nominal composition of 84% copper, 12% manganese and 4% nickel. Manganin has a resistivity of 0.45 to 0.50 x 10-6 Ohm-m (nearly 25 times that of copper) and develops a thermoelectric force against copper of 2 to 3 microV/°C. With proper heat treatment, it gives a suitable resistance value with time. The foremost property of manganin is that it has almost a zero temperature coefficient of resistance near about room temperatures. Manganin is used for resistances of very high accuracy when the temperature rise is not expected to rise above 15 to 20°C.

Constantan: These are a series of alloys of nickel and copper containing 40 to 60% nickel, with a small amount of manganese in order to improve their mechanical properties. All these alloys exhibit similar electrical properties. They are sold as constantan, or under various trade names for use as thermocouple materials. They have thermoelectric powers against copper of about 40 μ V per °C. However, except for their large thermoelectric powers, the electrical properties of these alloys are remarkably similar to those of manganin. Constantan has a resistivity at ordinary temperatures of about 25 times that of copper (about the same as manganin), it is corrosion resistant, inexpensive, and easy to work. This can be easily soft soldered to copper.

It finds extensive use in cases where its high thermoelectric power against copper is not a disadvantage. For example it is frequently used in resistors designed for a.c. operation. It also finds application in resistors of 1000 ohm and above as in voltmeter multipliers where the thermal emf generated at copper constantan junction is negligibly small as compared to the emf being measured.

Nickel Chromium Alloys: These alloys have a somewhat higher temperature co-efficient of resistance than that of manganin and constantan. Nichrome is an example of this class of alloys. These alloys cannot be used in precision resistances.

Nichrome has a very high resistivity (about 50 times that of copper) and resists corrosion even at very high temperatures. It is often used in rougher class of resistors, where small size is all important or where the operating temperatures are high. However, these alloys are difficult to solder.

Gold Chromium: This alloy appears to be very promising for some applications. It is made with slightly over 2 percent of chromium. This alloy has a resistivity at room temperature of about 20 times that of copper. Its temperature co-efficient can be made extremely small by baking it at fairly low temperatures. It has a thermo-electric power of 7 or 8 μ V per °C with copper. For many applications, the extremely small temperature coefficient of gold-chromium alloys make their use desirable. They are used for making heat resistant standard resistors. Although its resistance temperature co-efficient is small near room temperature the range over which the co-efficient is small is 20 to 30°C.

INDUCTORS

Standards of Inductance:

Both the self and mutual inductances depend upon their physical dimensions together with the number of turns in the coil. For the designing and construction of Inductance Standards, few considerations must be taken care of such as,

 (i)  The design and construction should be such that a rigidly standard accurate formula exists relating the value of inductance with the physical dimensions

(ii)  The design should be such that accurate measurement of physical dimensions is possible.

(iii) The materials used should be such that the value of inductance remains constant irrespective of the environmental and circuit conditions. This requires that

a. the materials used should be such that their dimensions do not change with time, temperature and humidity.

b. The inductance should be independent of the value of the current passing. This requires that no ferromagnetic materials be used. When we use ferromagnetic materials, the value of permeability and hence inductance is dependent upon flux density which in turn depends upon the current flowing in the coil. Hence the inductance of an inductor constructed with ferromagnetic cores depends upon the value of the current passing. In order for inductance to be independent of the current passing, air cored coils should be used for standards of inductance.

(iv)  The resistance of the windings should be very low as compared with their inductance or the inductor should have a high L/R ratio. The ratio of inductive reactance to resistance of a coil is known as its Storage Factor or Q Factor. The Q factor is defined as: Q=ωL/R

(v) The effective inductance and resistance should be least affected by frequency. This requires that there should be minimal losses. Ferromagnetic materials should never be used as eddy current losses in them are appreciable. The use of inductors having ferromagnetic cores is completely ruled out for high frequency application. The coils should use stranded wires as otherwise the eddy current losses in conductors become large especially at high frequencies. The use of metallic parts should be avoided as the eddy currents induced in them affect the value of inductance.

(vi) The inductor should be so designed that capacitive effects are negligible. This is particularly important for inductors working at high frequencies where the interturn capacitance may drastically change the effective value of inductance.

(vii) The inductor should be desirably unaffected by external magnetic fields and should produce a minimum interfering field of its own.

Formers for Inductance Coils: Marble is used for making formers or bobbins for the coils. The reasons for selecting marble are that it does not warp and is unaffected by atmospheric conditions. It has a high electrical resistance and hence acts like a perfect insulator. It is a non-magnetic material and can be easily machined. It is pretty cheap and is easy to work with.

Coils of Inductance Coils: The shape of the coils is manufactured such that a ratio of inductance to resistance is very high. The highest L/R ratio is obtained for a coil of circular shape with a square cross-section, with a mean diameter of coil about 3 times its depth. This can also be achieved by using larger weight of copper or by using an iron core.

CAPACITORS

Due to several factors, Capacitors do not show perfect and constant capacitance at all frequencies. There are ohmic losses in the plates and connecting wires, interfacial polarization and power loss in dielectric etc. Therefore, a capacitor can be represented by an equivalent circuit as shown in Fig. 1 (a). Resistance represents the losses. In the case of air and most other cases, the losses in the dielectric are very small and hence capacitors using these dielectrics may be regarded as perfect.

Fig. 1 (a) Equivalent circuit of Capacitor (b) Phasor diagram

Fig. 1 (b) represents the phasor diagram of a dielectric when a potential difference is applied across it. The various terms so used are defined as follows:

V = applied voltage; V

Ic = capacitive current; A

IR = active component of current; A

C = capacitance ; F

R = resistance; Ω

ω= 2πf; rad/s

f = frequency of supply; Hz

Power factor of a dielectric is the cosine of the angle between phasors representing the voltage across the dielectric and the total current through it when a sinusoidal AC voltage is applied across it.

Power factor cos ɸ = cos (90-δ) = sin δ.

δ  is called the loss angle of the capacitor. The value of δ very small therefore sin δ = tan δ = δ

Dielectric loss = VI cos (90-δ) = VI sin δ = V sin δ (I0/cos δ) = V I0 tan δ = ωCV2 tan δ

Where I0 = ωCV

Also, tan δ = IR/I0 = 1/ωCR

Fig. 2: (a) Capacitor equivalent circuit and (b) Phasor diagram

Fig. 2(a) shows the capacitor and 2(b) the phasor diagram for this arrangement of capacitor where

C = equivalent series capacitance; F,

r= equivalent series resistance; Ω.

Power loss= VI cos ɸ = VI sin δ = I2tan δ/ ωC

tan δ = Ir / (I/ωC) = ωCr

The power factor of a capacitor is very good test of its quality. A capacitor with a small dielectric loss and small leakage will have a very low power factor, i.e., a small loss angle. It is found that power factor (or tan δ) is practically constant over a wide range of frequency. tan δ is also known as dissipation factor of capacitor.

Dissipation factor, D = ωCr = 1/ ωCR

Capacitance Standards

Primary Standards. The dimensions of capacitance are those of length if the permittivity ε is taken as dimensionless. Therefore, values of primary standards of capacitance can be known by measuring lengths. The dimensions of such capacitors should be very accurately known in order that a primary standard is constructed. Air is usually used as the dielectric as it is the only dielectric whose permittivity is definitely known and which is free from absorption and dielectric loss.

Three types of constructions have been used for primary standards: (i) two concentric spheres. (ii) two concentric cylinders (iii) two parallel plates with guard rings

Parallel plate construction is normally not used; the concentric cylinder construction is shown in Fig. 3.

Fig. 3: Primary Capacitance Standard

Air capacitors have extremely low losses, usually assumed zero, if the dielectric which supports the insulated electrodes is good insulating material and is placed in a region of low field strength. Therefore, air capacitors seem at first consideration to be well suited as primary electrical standards. It has been found difficult, however, to secure the extremely high stability needed for this purpose. Even carefully treated metal parts warp somewhat with time and so permanency is not that much as is desired in primary standards.

Questionnaire

1. Resistors must show permanence with time and must be resistant to corrosion and oxidation. (True/ False)
2. Mutual inductance doesn’t depend on the number of turns. (True/ False)
3. In an inductor, the resistance of the windings should be very __________ as compared with their inductance.
4. For an inductor, Q factor is defined as __________.
5. Nickel Chromium alloy is used to prepare

(a) Capacitor

(b) Inductor

(c) Resistor

(d) None of the above

6. Formers of Inductance coils are made by

(a) Marbles

(b) Constantan

(c) Manganin

(d) None of the above

References:

1. Electronic Measurements and Instrumentation by Bernard M. Oliver and John M. Cage.
2. Measurement and Instrumentation Principles by Alan S. Morris.
3. Instrumentation and Measurement in Electrical Engineering by Roman Malaric.
4. Measurement and Instrumentation Systems by William Bolton.
5. Engineering Measurements and Instrumentation by Leslie Frank Adams.
6. Electrical Measurements and Instrumentation by U. A. Bakshi.
7. Introduction to Measurements and Instrumentation by Arun K Ghosh.