Series Connection of Batteries

Connection diagram :

The series connection of batteries is shown in Fig. 1(a). N number of identical batteries with terminal voltage of V volts and current capacity of I ampere each are connected in series. The load is connected directly across the series combination of N batteries as shown in Fig. 1(a). The load voltage is given by,

\[{{V}_{L}}=(V+V+……+V)\text{    }…..\text{N terms}\]

\[{{V}_{L}}=NV\text{ Volts}\]

However the series connection does not improve the current sourcing capacity. The current sourcing capacity of the series string is same as that of a single battery connected in the string, i.e. I amperes.

Figure 2. Series connection of batteries with different terminal.

It is not always necessary to connect all the batteries of same terminal voltages in series with each other. The batteries of different terminal voltages can be connected in series as shown in Fig. 2.

\[{{V}_{L}}={{V}_{1}}+{{V}_{2}}+{{V}_{3}}+{{V}_{4}}\]

Parallel Connection of Batteries

Connection diagram :

Figure 3.

The parallel connection of batteries is shown in Fig. 3. Batteries are connected in parallel in order to increase the current supplying capacity. If the load current is higher than the current rating of individual batteries, then the parallel connection of batteries is used. The terminal voltage of all the batteries connected in parallel must be the same. The load current is equal to the sum of currents drawn from the individual batteries.

\[{{I}_{L}}={{I}_{1}}+{{I}_{2}}+{{I}_{3}}+{{I}_{4}}\]

If all the batteries are of same current rating then they supply equal amount of current. But, if they are of different current ratings, then they share current in proportion with their current ratings.

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Working Principle of Thermistor

Thermistor have a Negative Temperature Coefficient (NTC) i.e. resistance decreases as the temperature increases. The materials used in the manufacture of thermistors include oxides of cobalt, nickel, copper, iron, uranium and manganese. The thermistor has very high temperature coefficient of resistance of the order of 3 to 5% per ºC. The resistance at any temperature T is given by,

\[{{R}_{T}}={{R}_{0}}\text{ exp }\beta \text{ }\left( \frac{1}{T}-\frac{1}{{{T}_{0}}} \right)\]

Where,

R_T – Thermistor resistance at temperature T (K)

R₀ – Thermistor resistance at temperature T₀ (K)

β – A constant determined by calibration

At high temperature, equation (1) reduces to,

\[{{R}_{T}}={{R}_{0}}\text{ exp }\left( \frac{\beta }{T} \right)\]

Working & Symbol of Thermistor

Figure 1.

The resistance-temperature characteristics is shown in Fig. 1 (b) and symbol in Fig. 1 (a). The curve is non-linear and the drop in resistance from 500Ω to 100Ω occurs for an increase in temperatures from 20 to 100ºC. The temperature of the device can be changed internally or externally. An increase in current through the device will raise its temperature carrying a drop in its terminal resistance. Any externally applied heat source will result in an increase in its body temperature and drop in resistance. This action tends itself well to control mechanisms.

Types of Thermistor

Figure 2: Various configurations of thermistor.

The thermistors are available in various configurations such as beads, disc, rod, washer as shown in Fig. 2. The smallest thermistors are made in the form of beads. Some are as small as 0.15 mm in diameter. And where greater power dissipation is required, thermistors obtained are in disc, washer or rod forms.

Advantages of Thermistor

1. Small size and low cost.
2. Fast response over narrow temperature range.
3. Good sensitivity in the NTC region.

Disadvantages of Thermistor

1. Non-linearity in resistance versus temperature characteristics.
2. Unsuitable for wide temperature range.
3. Very low excitation current to avoid self-heating.
4. Need of shielded power lines, filters etc. due to high resistance.

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Figure 1: Basic of Switch Mode Power supply (SMPS).

A switch mode power supply (SMPS) is a dc-to-dc series regulated power supply, in which the series pass transistor is operated as a switch. The output voltage of a SMPS is regulated by varying its duty cycle.

In SMPS, the series pass transistor (electronic switch in Fig. 1) does not operate in its active region. Instead it operates as a switch. This is how it is different from the conventional or linear power supply.

Block diagram of Switch Mode Power supply (SMPS)

The block diagram of a basic switching regulator is shown in Fig. 1. The block diagram shows that the SMPS is also a series regulator. The basic switch mode power supply consists of four components namely the unregulated dc voltage source V_in, an electronic switch S (a transistor or MOSFET), a pulse generator and a filter, as shown in Fig. 1.

Working of Switch Mode Power supply (SMPS)

The pulse generator generates rectangular pulses which are applied to the control terminal of an electronic switch. This switch is turned on and off with the help of these rectangular pulses. The switch is an electronic switch which is typically a transistor or MOSFET. It is used in its saturation and cut off regions and not in the active region. When the switch is on, it connects the unregulated dc input V_in as it is to the input of the filter and the filter input is disconnected from the dc input voltage V_in when the switch is open circuited.

Filter input voltage =  V_in        …..when switch is on

And, filter input voltage = 0       …..when switch is off

Figure 2: Waveforms of basic Switch Mode Power supply (SMPS).

This is shown in the waveforms of Fig. 2. Therefore at the input of the filter we get a rectangular waveform. The average value of this waveform can be adjusted by changing either the duty cycle or frequency of the rectangular pulses produced by the pulse generator. The duty cycle is defined as,

\[\text{Duty cycle (D) = }\frac{{{t}_{on}}}{{{t}_{on}}+{{t}_{off}}}=\frac{{{t}_{on}}}{T}\]

\[T={{t}_{on}}+{{t}_{off}}=\frac{1}{\text{Frequency}}\]

\[or\text{ T = }\frac{\text{1}}{f}\]

Typically, the operating frequency of the switching regulator will be in the range of 10 to 50 kHz. That means the total time T is of the order of 100 µs to 20 µs. The filter then converts the rectangular waveform at its input into a smooth dc voltage by removing the ripple contents. The expression for dc output voltage of a switching regulator is given by:

\[{{V}_{o}}=\frac{{{t}_{on}}}{T}\times {{V}_{in}}\]

\[or\text{   }{{V}_{o}}=D\times {{V}_{in}}\]

Thus the average output voltage is dependent on the duty cycle D. The average output voltage will increase with increase in the value of duty cycle as shown in Fig. 2.

Advantages of Switch Mode Power supply (SMPS)

The advantages of SMPS are as follows :

1. Low power dissipation in the series pass transistor as it operates as a switch and not in the active region.
2. High efficiency (upto 95%) due to reduced power dissipation in the transistor.
3. Small size : This is due to the smaller size of L and C at high operating frequencies and need of smaller heat sink for the series pass transistor.
4. Higher power handling capacity.

Disadvantages of Switch Mode Power supply (SMPS)

The disadvantages of SMPS are as follows :

1. Increased switching loss in the series pass transistor due to high frequency switching.
2. Radio Frequency Interference (RFD to the neighboring electronic circuits.
3. There is no isolation between input and output.
4. The load requires separate protection circuitry.
5. The transient response is slow as compared to the linear power supplies.
6. Ripple content in the output is higher than that for a linear power supply.
7. Load regulation is poor as compared to the linear regulators.

Difference between Linear regulator and Switch Mode Power Supply (SMPS) 

Types of Switch Mode Power supply (SMPS)

Figure 3: Classification of Switch Mode Power supply (SMPS).

The classification of SMPS is shown in Fig. 3. The SMPS are classified broadly into two categories namely :

1. Non-isolated type and
2. Isolated type.

No electrical isolation is provided between the load and source in the non-isolated type SMPS. Whereas, a transformer is included for providing the electrical isolation in case of the isolated type SMPS.

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When the anode terminal of a diode is connected to the negative terminal of voltage source and cathode to the positive terminal then the diode is reverse biased as shown in Fig. 1 (a) and its symbolic representation in Fig. 1 (b).

Operation of Reverse Biased PN Junction Diode

Figure 2: Reverse biased effect on layer and barrier voltage.

When an external bias is applied to a diode, positive to cathode and negative to anode, electrons from N-side are attracted to the positive terminal and holes from P-side are attracted to the negative terminal. As shown in Fig. 2, holes on P-side of junction are moved away from the junction and electrons are also moved away from the junction on N-side. This results in the depletion region to be widened and the barrier voltage to be increased.

As the barrier voltage at the junction increases, the holes and electrons are not able to cross the junction, hence the majority charge carrier current will be zero and the junction is said to be reverse biased. There will be very small reverse current due to minority charge carrier. Because of this very small reverse current flow, a reverse biased PN junction diode offers very high resistance. As there is no possibility of majority charge carriers the current flowing across a reverse biased junction, minority carriers i.e. holes on N-side and electrons on P-side, generated on each side can cross the reverse junction. The electrons on the P-side are attracted to the positive voltage crossing the junction on the N-side. The holes from N-side flow across to the negative voltage on P-side. Due to this, small current flows through the junction. Only a very small reverse bias voltage is necessary to move all available minority carriers across the junction and if voltage bias is increased further, current will not increase. And hence this current is referred as reverse saturation current. The reverse saturation current is very small ranging from nanoamperes to microamperes. It depends on the junction area, temperature and semiconductor material.

The post What is Reverse Bias of PN Junction Diode? appeared first on Electrical and Electronics Blog.

Figure 1.

When anode is connected to the positive terminal of a battery/voltage source and cathode to the negative terminal, then the diode is said to be forward biased as shown in Fig. 1 (a) and its symbolic representation is shown in Fig. 1 (b).

Operation of Forward Biased PN Junction Diode

Figure 2: Forward biased effect on layer and barrier voltage.

When PN junction is forward biased, the holes (being positively charged) are repelled by the positive terminal of voltage source and forced to move towards the junction. Similarly, the electrons (negatively charged) are repelled by the negative terminal of voltage source and move towards the junction. As they get some energy from the voltage source, some of the holes and electrons enter the depletion layer and recombine themselves. This results in reduction in width of depletion layer and the barrier potential with forward bias as shown in Fig. 2. Therefore, it causes a large current to flow through the diode. When the applied bias voltage is increased from zero, the barrier voltage gets decrease until it effectively disappears and majority charge carriers easily flow across the junction. The electrons from N-side are now attracted across to the positive bias terminal on P-side and holes from the P-side flow across to the negative terminal on the N-side. Thus, a majority carrier current flows and the junction is said to be forward biased. This large current due to majority charged carrier in forward biased is called as forward current.

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Figure 1: V-I Characteristics of a PN Junction Diode.

VI Characteristics of pn junction diode, is a graph between the voltage applied across the terminals of a device and the current that flows through it. Fig. 1 shows the V-I characteristics of a typical PN junction diode with respect to breakdown voltage (V_BR). The complete V-I characteristics is divided into two parts, namely forward characteristic and reverse characteristic.

Forward characteristics :

Figure 2.

Fig. 2 (a) shows the circuit arrangement for obtaining forward characteristic of a diode. In this circuit, the diode is connected to a d.c. voltage (V_AA) through the potentiometer (P) and a resistance (R). The potentiometer helps in varying the voltage applied across the diode. The resistance (R) is included in the circuit, so as to limit the current through the diode. A voltmeter is connected across the diode to measure the voltage and milliammeter to measure the current in the circuit. The positive terminal of the voltage source is connected to the anode and the negative terminal to the cathode, hence the diode is worked in forward-biased condition. Increase the voltage and record the corresponding values of diode current. The graph between applied voltage and current is plotted as shown in Fig. 2 (b).

Forward characteristics show that no current flow till the point P is reached. It is due to the fact that, applied voltage is less than the junction voltage i.e. 0.7 V for Silicon and 0.3 V for Germanium. As the voltage is increased above point P, the diode current increases rapidly. The voltage at which the diode starts conducting is called a knee voltage, cut-in voltage or threshold voltage. The knee voltage is denoted by V_R or V_γ. Its value is 0.6 V for Si and 0.2 V for Ge.

Reverse characteristics :

The circuit arrangement for obtaining reverse characteristics of a diode is shown in Fig. 3 (a). In the circuit a diode is connected in reverse biased condition i.e. cathode is connected to the positive terminal of voltage source and anode to the negative terminal. The applied reverse voltage is gradually increased above zero and the values of diode current are measured. The graph plotted between reverse voltage and current is shown in Fig. 3 (b). The curve OCD is called reverse characteristics of a diode. The reverse characteristics indicate that when applied reverse voltage is less than breakdown voltage (V_BR), the diode current is small and remains constant. This current is called as reverse saturation current (I_o).

When reverse voltage is increased to a large value, the diode reverse current increases as rapidly as shown by curve CD in Fig. 3. The applied reverse voltage at which large current flows through the diode is known as breakdown (V_BR) voltage of a diode.

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Construction and Symbol of Inductor

Figure 1: Inductor.

Fig. 1(a) shows the construction of an inductor and Fig. 1(b) shows its symbol. It is a fixed value inductor. An inductor consists of N turns of a laminated copper wire are wound around an iron core.

Unit of Inductor

Inductance is measured in Henry or millihenry or microhenry and it is denoted by L. Henry is a very large unit. Therefore millihenry and microhenry are the another small units used for inductors.

\[\text{1 mH = 1 }\times \text{ 1}{{\text{0}}^{-\text{3}}}\text{ H}\]

\[\text{1  }\!\!\mu\!\!\text{ H = 1 }\times \text{ 1}{{\text{0}}^{-6}}\text{ H}\]

The inductance of a coil is given by,

\[\text{L = }\frac{N\times \phi }{I}\]

Where,

N = Number of turns,

ϕ = Flux

I = Current through the coil.

So the factors affecting the inductance are number of turns, flux linkage and current.

Types of Inductor

Inductors are basically categories,

1. Fixed inductors.
2. Variable inductors.

1. Types of Fixed Inductor :

The fixed inductors are classified as follows:

1. Air-core inductor.
2. Iron-core inductor.
3. Ferrite-core inductors.

1. Air-core inductor :

(a) Symbol

(b) Construction

Figure 2: Air-core Inductor.

In this inductor, the coil is wound on a plastic or cardboard core. Therefore, effectively the air acts as core. The symbol of air core inductor is shown in Fig. 2.

Construction :

The construction of an air-core inductor is shown in Fig. 2. In the construction of air core inductors, a core is made up of ceramics, plastic or cardboard type insulating material. The conductive wire is wound on this core hence there is air inside the coil.

Applications :

1. They are used for intermediate or radio frequency (I.F. or R.F.) applications in tuning coils.
2. For inter-stage coupling.
3. IF. coils.
4. Iron-core inductor :

2. Iron-core inductor :

(a) Symbol

(b) Construction

Figure 3: Iron core Inductor.

An iron core inductor is a coil in which solid or laminated iron or other magnetic material forms a part or all of the magnetic circuit linking its winding. It is also known as iron-core choke. Iron core inductors have a high inductance value but they cannot operate at high frequency due to hysteresis and eddy current losses. Iron core increases the magnetic induction of a coil of wire. Because iron has high permeability, it allows more magnetic lines of flux to concentrate the core thereby increasing the electromagnetic induction.

Construction :

Iron core inductor consists of coil wound over a solid or laminated iron core. The construction of iron core inductor is shown in Fig. 3. The material used for the iron core inductor is Silicon steel which is composed of iron with some percent of silicon. The iron core is laminated to avoid eddy current losses. The laminated iron-core consists of thin iron laminations pressed together but insulated from each other. Low frequency iron cored chokes are used as filter chokes to smooth out ripple in the rectified ac supply amplifier stages and in other d.c. applications. The core materials most commonly used for smoothing chokes are, silicon iron laminations and grain oriented silicon iron.

Applications :

The iron core inductors are used in the dc power supply filter circuits and other low frequency applications.

3. Ferrite core inductor :

Figure 4: Ferrite core Inductor.

Ferrite is an artificially prepared non-metallic material using sintered iron oxide with other metal ions to control magnetic properties. If the coil of wire is wound on a solid core made of highly ferromagnetic substance called ferrite. Fig. 4 shows the symbol of ferrite core inductor. Ferrite is a ferrous magnetic material. In this type of inductor, wire is wound on a ferrite core.

Construction :

The construction of a ferrite core inductor is as shown in Fig. 4. Ferrites are ceramic materials composed of oxides of iron and other magnetic material. It is used at a high and medium frequency because it has high permeability with low loss, so it is more effective than iron core inductor. These inductors usually employ pot cores i.e. cores consisting of an outer cylinder with closed end. The winding is placed in annular space. The air- gap is introduced in the central core. We can choose a suitable length of this air gap, in order to change the properties of the pot to suit a wide range of design requirements.

Applications :

1. These are used at high and medium frequencies.
2. Ferrite rod antenna.

Specifications of inductor

1. Inductance value.
2. Q factor value.
3. Operating frequency range.
4. Power dissipation.
5. Core type.
6. Size and mounting requirements.
7. Stary capacitance.

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The overall gain of a multistage amplifier is the product of gain of individual stages.

\[A={{A}_{1}}\times {{A}_{2}}\times …..{{A}_{n}}\]

\[A=\frac{{{V}_{o1}}}{{{V}_{in1}}}\times \frac{{{V}_{o2}}}{{{V}_{in2}}}\times ……\times \frac{{{V}_{on}}}{{{V}_{inn}}}\]

Need of Cascade Amplifier

Amplification capacity of a single stage amplifier is limited and cannot meet the required specifications. A single stage amplifier uses limited transistor parameters because of which it cannot provide very high voltage and current gains and also it does not match its input impedance with the source and output impedance with the load. In order to overcome these limitations, two or more single stage amplifiers are connected in cascade. The cascade connection of amplifiers (i.e., multistage amplifiers) provides desired amplification.

N-stage Cascade Amplifier

Figure 2: n-stage cascaded CE amplifier.

The transistor circuit which involves more than one stage (or) multiple stages of amplification is called a multistage amplifier or cascaded amplifier. The block schematic of a multistage amplifier is shown in figure (1). The overall gain of a multistage amplifier is the product of gain of individual stages.

\[A={{A}_{1}}\times {{A}_{2}}\times …..{{A}_{n}}\] \[A=\frac{{{V}_{o1}}}{{{V}_{in1}}}\times \frac{{{V}_{o2}}}{{{V}_{in2}}}\times ……\times \frac{{{V}_{on}}}{{{V}_{inn}}}\]

Figure (2) illustrates the block schematic of an ‘n’ stage cascaded CE amplifier. The n-stages of the CE amplifiers are connected in such a way that, the output voltage of one amplifier is input to neighboring amplifier. The overall gain of an n-stage cascaded amplifier can be obtained as follows,

Voltage Gain (A_V): The general expression for the voltage gain of an amplifier circuit is given by,

\[{{A}_{V}}=\frac{\text{Output Voltage }}{\text{Input Voltage }}\]

Stage 1: Voltage gain of the first stage is expressed as,

\[{{A}_{v1}}=\frac{\text{Output Voltage of the first stage  }}{\text{Input Voltage of the first stage }}\]

\[{{A}_{V1}}=\frac{{{V}_{2}}}{{{V}_{1}}}\]

Stage 2: Voltage gain of second stage is expressed as,

\[{{A}_{V2}}=\frac{\text{Output Voltage of the second stage  }}{\text{Input Voltage of the second stage }}=\frac{{{V}_{3}}}{{{V}_{2}}}\]

Thus, the overall voltage gain of n-stage amplifier is the product of all the individual stages.

\[{{A}_{V}}=\frac{{{V}_{2}}}{{{V}_{1}}}\times \frac{{{V}_{3}}}{{{V}_{2}}}\times \frac{{{V}_{4}}}{{{V}_{3}}}……\times \frac{{{V}_{n}}}{{{V}_{n-1}}}\]

\[={{A}_{V1}}\times {{A}_{V2}}\times {{A}_{V3}}\times ……{{A}_{Vn}}\] \[{{A}_{V}}={{A}_{V1}}\times {{A}_{V2}}……\]

It can also be determined by using the relation,

\[{{A}_{V}}=\frac{{{A}_{1}}{{R}_{cn}}}{{{R}_{i1}}}\]

Where,

C₁ – Current gain of the ‘n’ stage amplifier

R_cn — Effective load impedance at the collector of n^th stage

R_il – Input impedance of first stage.

Current Gain (A_l): The general expression for current gain of an amplifier is given by,

\[{{A}_{I}}=\frac{\text{Output current }}{\text{Input current}}\]

Stage 1: The expression for current gain of first stage is given by,

\[{{A}_{I1}}=\frac{\text{Output current of the first stage  }}{\text{Input current of the first stage }}\]

\[=\frac{{{I}_{o}}}{{{I}_{b1}}}=\frac{-{{I}_{cn}}}{{{I}_{b1}}}\]

\[{{A}_{I1}}=\frac{-{{I}_{cn}}}{{{I}_{b1}}}\]

Where,

\[\frac{-{{I}_{cn}}}{{{I}_{b1}}}\text{ }-\text{ Base to collector gain of the first stage}\]

Stage 2: The expression for current gain of second stage is given by,

Therefore the overall current gain of an ‘n’ stage amplifier is expressed as,

\[{{A}_{I2}}=\frac{{{I}_{b1}}}{{{I}_{c1}}}=\frac{{{I}_{c2}}}{{{I}_{c1}}}…..\frac{{{I}_{cn}}}{{{I}_{{{c}_{n-1}}}}}\]

\[{{A}_{l}}={{A}_{I1}}\times {{A}_{I2}}\times ……\]

Power Gain (A_P): The power gain of an n-stage cascade amplifier is given as,

\[{{\overline{A}}_{p}}=\frac{\text{Output power of last or }{{\text{n}}^{\text{th}}}\text{stage  }}{\text{Input power of the first stage }}\]

\[=\frac{{{\overline{V}}_{o}}{{\overline{I}}_{o}}}{{{\overline{V}}_{1}}{{\overline{I}}_{b1}}}\]

\[{{\overline{A}}_{p}}={{\overline{A}}_{V}}.{{\overline{A}}_{l}}\]

Thus, the overall gain of an n-stage cascade amplifier is  \({{\overline{A}}_{p}}={{\overline{A}}_{V}}.{{\overline{A}}_{l}}\).

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Working Principle of Strain Gauge

Their working principle is based on piezo-resistive effect. The piezo-resistive effect states that if a metal conductor is stretched or compressed, its length and diameter changes. Therefore its resistance also gets changed. Similarly the resistance of a metal conductor changes when it is strained.

Fig. 1 shows an unstrained wire of elastic material with length L, Diameter: D and Area of cross-section = A.

\[R=\rho \frac{L}{A}=\rho \frac{L}{(\pi /4){{D}^{2}}}\]

\[R=\rho \frac{L}{A}=\rho \frac{L}{\left( \frac{\pi }{4} \right){{D}^{2}}}\]

Where,

ρ = Resistivity of the wire in Ω – m

If this wire of elastic material (Strain Gauge) is subjected to tension, its length increases and diameter reduces. These changes in the dimensions due to applied force are shown in Fig. 2.

Let the change in length = ΔL and change in diameter = ΔD. To find the change in resistance (ΔR) due to applied force we use Poisson’s ratio.

\[\text{Using Poisson ratio (}\mu \text{) = }\frac{(\Delta D/D)}{(\Delta L/L)}\]

But,

\[\frac{\Delta L}{L}=\sigma =\text{ Strain}\]

Therefore,

\[\Delta D=\mu .\sigma .D\]

Thus the change in resistance is given by ΔR = Rσ (1+2µ).

From the above equation, we can conclude that the resistance of the wire increases due the applied force. The gauge factor (G) of a strain gauge is defined as the unit change in resistance per unit change in length. Therefore,

\[G\text{= }\frac{(\Delta R/R)}{(\Delta L/L)}\] (Ranges from 1.5 to 1.7)

Types of Strain Gauge

The two types of strain gauges as

1. Bonded Strain Gauge
2. Unbonded Strain Gauge

Bonded Strain Gauge

Fig. 3: Bonded Type Strain Gauge.

A bonded strain gauge consists of a grid of fine wire which is fixed on a base of a thin paper sheet as shown in Fig. 3. The paper sheet is bonded with an adhesive to the spot under measurement. When force is applied to the surface, to which the strain gauge is bonded, the resistance of the grid wire changes due to the change in length and diameter of the wire. This change in the resistance can be measured by connecting the strain gauge in one of the arms of the Wheatstone bridge that generates equivalent voltage. The bonded strain gauge is useful only for measuring very small displacements. To measure large displacements, the strain gauge is bonded to a flexible element like cantilever beam. The displacement can then be measured at the end of the cantilever beam.

Unbonded Strain Gauge

Fig. 4: Unbonded Type Strain Gauge.

As shown in Fig. 4, an unbonded strain gauge is constructed by fitting the gauge wire on a stationary frame having a movable armature fixed at the centre. The armature can be moved only in one direction and its travel is limited by four strain gauge wires. If an external force is applied to the strain gauge or the armature is moved, the gauge wire gets stretched showing a proportional change in its resistance value which can be measured with the Wheatstone bridge. The output voltage of the Wheatstone bridge can be calibrated according to displacement of the armature.

Advantages of Strain Gauge

1. High accuracy and reliability.
2. Small size and easy to use.

Disadvantages of Strain Gauge

1. High cost.
2. The changes in temperature may affect the output.

The post What is Strain Gauge? Working Principle, Diagram, Types, Derivation & Formula appeared first on Electrical and Electronics Blog.

Figure 1. Force acting on a Current Carrying Conductor placed in a Magnetic Field.

It is observed that whenever a current carrying straight conductor is placed in a magnetic field, it experiences a mechanical force. This is a very important magnetic effect of an electric current as the operation of the electric motors and other electrical appliances is entirely based on this effect. The magnitude of this force is dependent on the following factors:

1. Flux density (B) of the magnetic field in which the conductor is placed (in tesla).
2. Magnitude of the current (I) in the conductor (in amperes).
3. Active length (l) of the conductor (in metres). Active length is the part of the total length of the conductor which actually lies in the magnetic field.

If the conductor is at right angles to the magnetic field, then this force (F) is given by the following expression :

\[\text{F=B I }l\text{ newton}….(1)\]

It will be interesting to see how this force is actually produced. Fig. 1 (a) shows a straight conductor carrying current in the direction towards the observer and placed in a uniform magnetic field at right angles to it. The original field and that due to the conductor are also shown in Fig. 1 (a). These two fields combine to form a single resultant field. It will be seen that in the region below the conductor, both the fields act in the same direction and therefore give a resultant field at any point equal to the sum of the individual fields at that point. In the region above the conductor, one field acts in the direction opposite to that of other and so the resultant is the difference of the two fields. In general, the original field of the magnet is strengthened at the bottom of conductor and weakened at the top. The resultant field pattern is shown in Fig. 1 (b) effect, it seems as if some of the lines of force from the top region are transferred to bottom region.

Due to crowding, the lines of force in the lower region get stretched like rubber bands. Therefore, they try to contract and thereby push the conductor upwards. Thus, conductor experiences a mechanical force in the upward direction. If the direction of the current in the conductor or the direction of the main field reversed, the direction of force exerted on the conductor is also reversed. The direct of the force can be easily found by Fleming’s left hand rule.

Fleming’s Left Hand Rule :

Arrange the first finger, the second finger and the thumb of your left hand mutually at right angles to one another (Fig. 1 c). Point the first finger in the direction of the field and the second finger in the direction of the current, then the thumb will point in the direction of the force on the conductor.

On applying the above rule to the conductor which we have considered, it will be readily found that it experiences a mechanical force in the upward direction. In general, if the current carrying conductor under consideration in the above case is assumed to be making an angle θ with the direction of the field, then the Expression (1) for the force experienced by it will obviously get modified as follows :

\[\text{F = B I }l\text{ sin}\theta \text{ newton}\]

Where,

l sinθ = Component of the active length of the conductor at right- angles to the flux.

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