Electrical Resistance

Electrical resistance definition and calculations.

• Resistance definition
• Resistance calculation
  • Resistance calculation with Ohm's law
  • Temperature effects of resistance
  • Resistance of resistors in series
  • Resistance of resistors in parallel
• Measuring resistance
• Superconductivity

Resistance definition

Resistance is an electrical quantity that measures how the device or material reduces theelectric current flow through it.

The resistance is measured in units of ohms (Ω).

If we make an analogy to water flow in pipes, the resistance is bigger when the pipe is thinner, so the water flow is decreased.

Resistance calculation

The resistance of a conductor is resistivity of the conductor's material times the conductor's length divided by the conductor's cross sectional area.

R is the resistance in ohms (Ω).

ρ is the resistivity in ohms-meter (Ω×m)

l is the length of the conductor in meter (m)

A is the cross sectional area of the conductor in square meters (m²)

It is easy to understand this formula with water pipes analogy:

• when the pipe is longer, the length is bigger and the resistance will increase.
• when the pipe is wider, the cross sectional area is bigger and the resistance will decrease.

Resistance calculation with ohm's law

R is the resistance of the resistor in ohms (Ω).

V is the voltage drop on the resistor in volts (V).

I is the current of the resistor in amperes (A).

Temperature effects of resistance

The resistance of a resistor increases when temperature of the resistor increases.

R₂ = R₁ × ( 1 + α(T₂ - T₁) )

R₂ is the resistance at temperature T₂ in ohms (Ω).

R₁ is the resistance at temperature T₁ in ohms (Ω).

α is the temperature coefficient.

Resistance of resistors in series

The total equivalent resistance of resistors in series is the sum of the resistance values:

R_Total = R₁+ R₂+ R₃+...

Resistance of resistors in parallel

Measuring electrical resistance

Electrical resistance is measured with ohmmeter instrument.

In order to measure the resistance of a resistor or a circuit, the circuit should have the power supply turned off.

The ohmmeter should be connected to the two ends of the circuit so the resistance can be read.

Superconductivity

Superconductivity is the drop of resistance to zero at very low temperatures near 0ºK.

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Transistors

The word "transistor" was chosen to describe the function of a three terminal PN junction device that is able to amplify signal. It has a characteristics of "transferring current across resistor". It was invented by Schockley, Bardeen and Brattain at Bell Labs in 1947 and today has revolutionized the way we live. Our microprocessor consists of millions of trans. house in a device called integrated circuit.

Trans. work on the principle that certain materials such as silicon, can be made to perform as "solid state" devices. Any material is only conductive in proportion to the number of "free" electrons that are available. Silicon have very few free electron but if "impurities" such as arsenic are introduced in a controlled manner then the free electrons or conductivity is increased.

By adding other impurities such as gallium, an electron efficiency or hole is created. As with free electrons, the holes encourage conductivity and the material is called a semi-conductor.Semiconductor material which conducts by free electrons is called n-type material while material which conducts by virtue of electron deficiency is called p-type material.

They fall into the category of bipolar trans., either the more common NPN bipolar or the PNP types. There is another type known as a FET which has high input impedance with its characteristics comparable to valves. Modern field effect trans. or FET's include JFETS and MOSFETS.

Transistor Types

A silicon NPN Voltage(base-emitter) needs to be forward biased by about 0.65V for it to turn on. Figure 1 shows the 2 types of trans. which is PNP and NPN types. In PNP type, the emitter is made positive with respect to both the collector and base and the collector is made negative with respect to both the emitter and base in normal operation. It is the reverse for NPN type.

Characteristics

An important characteristics of a trans.  is its Beta or current amplification factor which is expressed as HFE(static forward current transfer ratio) or hfe(small signal forward current transfer ratio). Both relates to the grounded emitter configuration.

Beta is the ratio of the collector current to its base current, Beta= Ic/Ib.

Therefore if the base current of 1mA causes the collector current to rise to 50mA, the beta is 50. Typical junction trans. beta is in the range of 10 to several hundreds.

Alpha is the ratio of collector to its emitter current, Alpha = Ic/Ie. It is expressed as HFB(static forward current transfer ratio) or hfb(small signal forward current transfer ratio).

The smaller the base current, the closer the collector current comes to equal with the emitter current and the closer alpha comes to equal to 1. Typical value of alpha for junction trans. is between 0.92 and 0.98.

The collector current depends on the emitter current and is independent of the collector voltage. The separation between the curves is quite uniform which means that almost distortionless output can be obtained over the useful operating range of the transistor. 

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Heat Sink

Any electronics design engineer sooner or later will face problems related to the heat that is produced in semiconductor devices. When a junction temperature of a semiconductor rises above its maximum allowable temperature, there is a need to dissipate this temperature or else the device will breakdown.

One of the common method used to dissipate the heat is using a heat sink(HS). HS is made of metal which is used to contact the hot surface of the electronic component.

It usually consists of a flat base with an array of comb or fin protrusions which increase the surface area of its contact with the air. The greater the surface area, the better it is able to dissipate the heat generated.

The cooling methods used could be natural air convection, forced air convection or forced liquid convection. Force air convection is usually done by using a fan to aid the cooling process. Most of power electronics devices such as IGBT, Triac, power transistors, voltage regulators will require a HS. Other devices that need HS as a source of thermal transfer are the microprocessors used in the computers and digital signal processors.

A thermally conductive grease compound is usually used between the surface of the device and the electronic device to ensure good thermal contact.

Material

The material is usually made of aluminium, cooper or a combination of aluminium and cooper. Aluminium is light and has a typical thermal conductivity of 200W/mK. Cooper has a thermal conductivity twice that of Aluminium and the typical value is 400W/mK.

This make cooper a better choice for use as HS. However, due to its weight, higher price and higher production cost, the Aluminium is a preferred choice. Aluminium is light, soft, and the production cost is lower as it can be extruded easily.

The Aluminium is made harder by the treatment of almite processing (Anodizing). The surface of it can also by dye with colors such as black, silver or gold. Anodize will help to produce a layer of insulating coating that helps to prevent corrosion.

Characteristics

How does one design or choose a good HS? The typical characteristics are as listed below.

• Heat dissipation is proportional to the surface area of its fins. Hence, it should be designed to have large surface.
• Heat dissipation is proportional to the temperature difference between the device and the ambient temperature.
• Flat surface contact with the heat source is critical as it allows the use of a layer of thermal compound to reduce the thermal resistance between the two devices.
• Forced convection by fan increases the cooling performance by more than 2 times compared to the natural convection. The design of the heat sink must allow for the air to easily flow through the fins.
• The way the mounting is done is critical. Mounting using screws are better than using clips, sticky tape or glue.

Calculation

HS performance is measured in °C/W and is called thermal resistance. If a thermal load of 50W is applied toa heat sink which causes the temperature of the heat source to rise by 20 °C, the HS has a rating of 20/50 °C/W = 0.25 °C/W

Example of a calculation.

Find the maximum operating temperature of a power transistor if the maximum junction temperature Tj= 150 °C, thermal resistance between junction and case RJC = 1.5 °C/W, Power consumption P = 6W, thermal resistance between heat sink and the ambient RHA = 8.0 °C/W, Mica insulation RCF = 1.0 °C/W.

The maximum ambient temperature that this transistor can operate is: 

TA = Tj - (RJC + RCF + RHA)P 

= 150°C - (1.5 + 1.0 + 8.0)6 °C

= 150°C - 63°C 

= 87 °C

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Batteries

Batteries can be divided into two categories. The primary type is intended for one time use only and is disposed after the charge has dropped to a level that cannot be used. Primary type should not be discharged as heat will be generated within sealed cells.

It will also damage the equipment as a consequent of fluid leakage. The storage or secondary type can be recharged many times and is reusable.

The rating of its capacity is ampere hours (Ah) which is a product of current drain and time.

If it become cold, it will have less charge available and some design to keep it warm before use. It may lose 70% of its capacity at cold extremes but will recover with warmth.

Primary Type

Carbon zinc is the most common primary cell in which the chemical oxidation converts the zinc into salts and electricity. When there is no current flowing, the oxidation stops. If keep for a long period of time, the stored cell will degrade and dry out where it will no longer able to supply the desired current. The time taken for the degradation without being used is called shelf life. It has a nominal voltage of 1.5V.

Alkaline types have longer capacity at low temperatures. Lithium type have nominal voltage of 3V/cell and has the best capacity, discharge, shelf life and temperature characteristics. Its setback is the high cost.

Silver Oxide and Mercury has voltages of 1.5 V and 1.4 V respectively and are used where constant voltage is desired at low currents over a long period of time. Their main used and applications are in hearing aids.

Storage Type

The most common type is nickel-cadmium(Ni-Cd) type with a nominal voltage of 1.2V/cell. If used carefully, it can be rechargeable up to 500 times compared to alkaline type which is 50 times or so.

The most widely used storage type is the lead-acid type in automobile.The Lead Acid battery is made up of plates, lead, and lead oxide with a 35% sulfuric acid and 65% water solution.

Gas escaping from it may be explosive and always keep flame away. It should not be subjected to unnecessary heat, vibration or physical shock. Frequent inspections for leak is recommended. The electrolyte is chemically active and conductive and may ruin electrical equipment if leaks occurred. Its acidity may be neutralized with sodium bicarbonate or baking soda.

In order to ensure that all the cells in NiCd reach a fully charged condition, it should be charged by a constant current of 0.1 C current level. It is around 50 mA for a AA size cells. Charging should be terminated after 15 hours at the slow rate. A built in circuit that will stop charging when 1.43V/cell is reached will enhance the life of the battery. 

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