Equipments for Electroplating

Figure 1: Electroplating.

Fig. 1 shows a small electroplating plant with the following equipments.

Electroplating Tank : For the solutions employed in electroplating, chemically resistant containers are generally necessary. Welded steel tanks suitably lined are used for the majority of electroplating processes. Wooden, R.C.C., fibre glass, stainless steel and enamelled iron tanks are also in use. The lining materials include lead, rubber, P.V.C. etc. The tank is filled with suitable electrolyte and has arrangement for hanging anodes and articles to be plated which normally form cathode. Apart from the electrolyte, some additional reagents like glue, gum, sugar, etc. are also added to obtain good results.

Power Supply Unit : For electroplating, direct current ranging from 50 to 1000 amperes or even more at 3 to 24 volts is required. Static rectifiers are normally employed for this purpose.

General Procedure for Electroplating

Before electroplating, the object must be perfectly clean, free from dirt, paint, scales, rust, grease, oil, etc.

• Cleaning is carried out using solvents like paraffin, hot alkaline cleaners (e.g. caustic potash) and acids.
• For smooth surface, mechanical operations like grinding, polishing are also carried out if necessary.

The object is then dipped in the bath for electroplating. The actual process of deposition of metal on the object forming the cathode by electrolysis has already been discussed previously. The metal to be deposited is supplied either by the anode of that metal or the electrolyte itself. The cathode (the article to be plated) is surrounded by the set of anodes or it is rotated slowly to ensure an even deposit all over. As a general rule, slower the deposition, the harder and more adherent it is. Hence, small currents are employed. The concentration and temperature of the electrolyte are other vital factors which affect the quality of the plating. Plating time depends on the mass of metal to be deposited. After plating, the article is washed and dried. In the cases of nickel, silver and chromium plating, the plated article is finally buffed with polishing mop rotated at high speed, for a bright metallic finish.

Applications of Electroplating

Gold or silver plating is many times done for decorative or ornamental purposes. The cast iron and steel parts are normally coated with zinc, nickel or chromium to prevent atmospheric corrosion. Nickel or chromium plating also gives shining white surface. Copper plating is mostly used on iron articles to prevent rusting or as preliminary coating for nickel or silver plating.

The post What is Electroplating? Process, Parts & Diagram appeared first on Electrical and Electronics Blog.

Electrolysis Process

Figure 1: Electrolysis.

To understand the process of electrolysis, consider the solution of copper sulphate (CuSO₄) in water. As the moment, copper sulphate (CuSO₄) is dissolved in water, its molecules dissociate into positively charged copper (Cu) ions and negatively charged sulphate (SO₄) ions. The ions thus formed start wandering freely in the solution.

Now, if two electrodes (P and K) are immersed in the solution and a battery (B) is connected as shown in Fig. 1, let us see the result. As soon as the potential difference is applied across the electrodes with the help of the battery, the haphazard movement of the ions becomes a directed movement. The positive copper ions are attracted to the negative electrode (K) called cathode, and the negative sulphate ions to the positive electrode (P) called anode.

On reaching the respective electrodes, they give up their charges and become ordinary molecules. Thus the copper ions become ordinary molecules of copper, which are deposited on the cathode. The sulphate ions also become ordinary sulphate molecules at the anode.

As the uncharged sulphate ion is incapable of separate existence, it immediately reacts with water (H₂O) forming sulphuric acid (H2SO₄) and liberating oxygen gas (O₂) at the anode. The chemical reaction can be stated as follows :

\[2S{{O}_{4}}=2{{H}_{2}}O=2{{H}_{2}}S{{O}_{4}}+{{O}_{2}}\uparrow \]

If the anode is a suitable copper plate, the sulphate ion acts on it to form copper sulphate as given below :

\[S{{O}_{4}}=Cu=CuS{{O}_{4}}\]

This newly formed copper sulphate goes into solution and thus the density of the electrolyte is maintained constant. The net effect is that the copper from the anode is transferred to the cathode. The above process involving chemical decomposition of the electrolyte due to passage of current is known as electrolysis. It should be noted that the conduction of current in electrolyte is due to oppositely directed movements of positive and negative ions and it is always accompanied by a chemical change.

Faraday’s Laws of Electrolysis

In 1834, Faraday formulated following two basic laws based on his experimental work on electrolysis.

First Law

It states that the weight of a substance liberated from an electrolyte in a given time during the process of electrolysis is directly proportional to the quantity of electricity which has assed through the electrode.

Thus, if

W = Weight of the substance liberated in kg

Q =  Quantity of electricity in coulombs

= Current (I) in amperes × Time (t) in seconds. Then, according to this law,

\[W\propto Q\propto I.t\]

Or,

\[W=Z.I.t\]

Where, Z is a constant called the electrochemical equivalent.

It is defined as the mass of the particular substance liberated in unit time by unit current and its unit is the kilogram per coulomb.

Second Law

It states that if the same current flows through several electrolytes, the weights of the substances liberated from each are proportional to the chemical equivalents of these substances.

The chemical equivalent of a substance is the weight of the substance which can displace or combine with unit weight of the substance in a chemical reaction.

With the above definition, the chemical equivalent of hydrogen itself will be obviously one.

Extraction and Electro refining of Metals

The metals like aluminium, copper, magnesium, sodium, zinc, etc. can be extracted from their ores and refined by electrolytic processes.

In electrolytic extraction process, the ore is either melted or treated with strong acid. The pure metal is then obtained by the electrolysis of this solution. The metals obtained by electrolytic extraction methods being 98 to 99 percent pure, these methods are always preferable in comparison with the other metallurgical processes available for the most of these metals. Sometimes, however, this electrolytic extraction cannot be carried out economically. Therefore, in such cases, only the refining is done electrolytically.

Copper is extracted by metallurgical as well as electrolytic processes. However, it is always refined electrolytic ally to its purest form as required by the electrical industries. For refining of metals, ingots of impure metal obtained from metallurgical process are used as anodes. They are placed in an electrolytic cell containing a suitable electrolyte. The current is then passed through the bath. Due to electrolysis, the pure metal gets deposited on the cathode made of pure metal.

Power Supply: Large amount of d.c. power is required for extraction and refining of metals. Voltage per electrolytic cell is only about 10 V. However, a number of such cells can be connected in series, so that the voltage required is 500 to 800 volts, with currents upto several thousand amperes. Special heavy current motor-generator sets, rotary convertors or mercury arc rectifiers are used for conversion of a.c. to d.c.

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Operation of Transformer On load

Figure (1) shows a transformer with a load connected across the secondary winding. The load current I₂ flowing through the secondary turns sets up its own m.m.f N₂I₂ which produces the flux ϕ₂.

According to Lenz’s law this flux is in such a direction that it opposes the flux ϕ, produced by the m.m.f N₁I₀ which is set up by the no-load current I₀ flowing throw the primary turns. Consequently the flux is momentarily reduced due to opposing flux ϕ. This in turn causes reduction in induced e.m.f (E₁) in primary according to Faraday’s law E₁ reduces, the difference between applied voltage (V₁) and E₁ increases.

Consequently, the primary will draw more current. Consider \({{{I}’}_{1}}\) to be this additional primary current. It is also known as counter balancing current as it balances between applied voltage and primary e.m.f or it is known as load component of primary current and it is antiphase with secondary current I₂. Now this current \({{{I}’}_{1}}\) sets up its own m.m.f N₁\({{{I}’}_{1}}\) which produces the flux and it is equal in magnitude in such a direction that it opposes the flux ϕ₂. Hence ϕ’₁ and ϕ₂ cancel each other and only flux ϕ flows in the core. Therefore the total flux produced during loaded condition is approximately equal to the flux at no-load.

\[{{\phi }_{2}}=-{{{\phi }’}_{1}}\]

As secondary ampere turns of I₂ are neutralized by primary ampere turns of \({{{I}’}_{1}}\).

\[{{N}_{2}}{{I}_{2}}={{N}_{1}}{{{I}’}_{1}}\]

\[{{{I}’}_{1}}=\frac{{{N}_{2}}}{{{N}_{1}}}{{I}_{2}}\]

The net primary current is the vector sum of primary counter balancing current \({{{I}’}_{1}}\) and the no-load current I₀.

\[{{I}_{1}}={{{I}’}_{1}}+{{I}_{0}}\]

Since the no-load current I₀ is very small compared to the counter balancing current \({{{I}’}_{1}}\), therefore the net primary current is approximately equal to the current \({{{I}’}_{1}}\).

\[{{I}_{1}}={{{I}’}_{1}}\]

\[=\frac{{{N}_{2}}}{{{N}_{1}}}{{I}_{2}}=K{{I}_{2}}\]

‘K’ represents transformation ratio.

\[\frac{{{I}_{1}}}{{{I}_{2}}}=\frac{{{{{I}’}}_{1}}}{{{I}_{2}}}=\frac{{{N}_{2}}}{{{N}_{1}}}=K\]

\[{{I}_{1}}=K{{I}_{2}}={{{I}’}_{1}}\]

Therefore, the primary and secondary currents are inversely proportional to their turns ratio. The total primary current is in anti-phase with I₂ and K times the current I₂.

Phasor Diagram of Transformer with Resistive Load

The phasor diagram for resistive load is drawn as shown in the following figure (2). For purely resistive load, the secondary load current I₂ is in phase with the secondary’ terminal voltage V₂. The counter balancing current \({{{I}’}_{1}}\) is in opposition and equal in magnitude with the secondary load current I₂. The primary current I₁ is the vector sum of \({{{I}’}_{1}}\) and no-load current I₀ respectively. I₀ lags behind V₁ by no-load power factor angle ϕ₀ and I₁ lags behind the voltage V₁ by primary power factor angle ϕ₁.

The post Transformer on Load – Circuit Diagram & Phasor Diagram appeared first on Electrical and Electronics Blog.

When the transformer is on no-load, the secondary winding is opened as in figure (a) and current I₂ is zero. In this condition, the primary winding draws a no-load current ‘I₀‘ which has two components i.e.,

1. Magnetizing component (I_µ), and
2. Working component (I_w).

1. Magnetizing Component (I_µ) :

It lags behind the applied voltage on primary winding ‘V₁‘ by 90º. It is also called as reactive or wattless component of no-load current and is responsible to develop an e.m.f to maintain the flux ‘ϕ’ in the core. It is expressed as \({{I}_{\mu }}=\text{ }{{I}_{0}}\sin {{\phi }_{0}}\).

2. Working Component (I_w) :

It is in phase with the primary applied voltage ‘V₁‘. The component is also called as active component or iron loss component, and is used for describing the core losses such as hysteresis loss and eddy current loss. It is expressed as \({{I}_{w }}=\text{ }{{I}_{0}}\cos {{\phi }_{0}}\).

From the phasor diagram of figure (b),

\[\sin {{\phi }_{0}}=\frac{{{I}_{\mu }}}{{{I}_{0}}}\]

Thus, \({{I}_{\mu }}={{I}_{0}}\sin {{\phi }_{0}}\) is the reactive component of no-load current I₀ and

\[\cos {{\phi }_{0}}=\frac{{{I}_{w }}}{{{I}_{0}}}\]

Thus, \({{I}_{w }}={{I}_{0}}\cos {{\phi }_{0}}\) is the active component of no load current I₀.

Hence,

\[{{I}_{0}}=\sqrt{I_{w}^{2}+I_{\mu }^{2}}\]

cosϕ₀ is the no-load power factor and ϕ₀ is the hysteresis angle of advance.

The post Transformer on No Load – Circuit Diagram & Phasor Diagram appeared first on Electrical and Electronics Blog.

Consider the two winding single-phase transformer shown in figure (1).

\({{{I}}_{1}}\) = Current in the primary

\({{{E}}_{1}}\) = Induced e.m.f in the primary

\({{{V}}_{1}}\) = Voltage applied to the primary

\({{{I}}_{2}}\) = Current in the secondary

\({{{E}}_{2}}\) = Induced e.m.f in the secondary

\({{{V}}_{2}}\) = Terminal voltage of secondary

Here, the primary current \({{{I}}_{1}}\) has two components, one is no-load primary current, \({{{I}}_{0}}\) and the other one is load component of primary current \({{{I}’}_{2}}\). The function of current \({{{I}’}_{2}}\) is to counter balance the secondary current \({{{I}}_{2}}\). The no-load primary current \({{{I}}_{0}}\) leads to the production of losses in the core while magnetizing the core of the transformer. The no- load primary current \({{{I}}_{0}}\) can be resolved into two components i.e., active (or) working component I_w and reactive (or) magnetizing component ‘I_µ‘. The working component ‘I_w’ of no-load current \({{{I}}_{0}}\) leads to the core loss, hence it can be represented by a resistance R₀. The magnetizing current ‘I_µ‘ produces flux which induces e.m.f E₁.

The reactance due to flux is represented by X₀. To account for the core loss and the magnetizing current, an equivalent circuit can be represented by a shunt branch in the primary side as shown in the figure (2).

\[\text{Core loss = }I_{w}^{2}{{R}_{0}}=\frac{E_{1}^{2}}{{{R}_{0}}}\]

To make transformer calculations simpler, transfer voltage, current and impedance either to the primary or secondary

Equivalent Circuit of Transformer as Referred to Primary Side

Secondary parameters transferred to primary side are given as follows,

\[{{{R}’}_{2}}=\frac{{{R}_{2}}}{{{K}^{2}}}\]

\[{{{X}’}_{2}}=\frac{{{X}_{2}}}{{{K}^{2}}}\]

\[{{{Z}’}_{2}}=\frac{{{Z}_{2}}}{{{K}^{2}}}\]

\[{{{I}’}_{2}}=K{{I}_{2}}\]

\[{{{E}’}_{2}}=\frac{{{E}_{2}}}{K}\]

\[{{{V}’}_{2}}=\frac{{{V}_{2}}}{K}\]

Where,

\[K=\frac{{{N}_{2}}}{{{N}_{1}}}\]

We know that,

\[{{R}_{01}}={{R}_{1}}+{{{R}’}_{2}}={{R}_{1}}+\frac{{{R}_{2}}}{{{K}^{2}}}\]

\[{{X}_{01}}={{X}_{1}}+{{{X}’}_{2}}={{X}_{1}}+\frac{{{X}_{2}}}{{{K}^{2}}}\]

\[{{Z}_{01}}=\sqrt{R_{01}^{2}+X_{01}^{2}}=\frac{{{Z}_{02}}}{{{K}^{2}}}\]

The equivalent circuits referred to primary side are as shown in figures (3) and (4).

Equivalent Circuit of Transformer Referred to Secondary Side

Primary parameters transferred to secondary side are given as follows,

\[{{{R}’}_{1}}={{K}^{2}}{{R}_{1}}\]

\[{{{X}’}_{2}}={{K}^{2}}{{X}_{1}}\]

\[{{{Z}’}_{1}}={{K}^{2}}{{Z}_{1}}\]

\[{{{E}’}_{1}}=K{{E}_{1}}\]

\[{{{V}’}_{1}}=K{{V}_{1}}\]

\[{{{I}’}_{1}}=\frac{{{I}_{1}}}{K}\]

\[{{{I}’}_{0}}=\frac{{{I}_{0}}}{K}\]

\[{{{R}’}_{0}}=\frac{{{R}_{0}}}{{{K}^{2}}}\]

\[{{{X}’}_{0}}=\frac{{{X}_{0}}}{{{K}^{2}}}\]

We know that,

\[{{R}_{02}}={{R}_{2}}+{{{R}’}_{2}}={{R}_{2}}+{{K}^{2}}{{R}_{1}}\]

\[{{X}_{02}}={{X}_{2}}+{{{X}’}_{1}}={{X}_{2}}+{{K}^{2}}{{X}_{1}}\]

\[{{Z}_{02}}=\sqrt{R_{02}^{2}+X_{02}^{2}}={{K}^{2}}{{Z}_{01}}\]

The equivalent circuit diagrams referred to secondary side are shown in figure (5) and figure (6).

The post Equivalent Circuit of Transformer – Circuit Diagram & Derivation appeared first on Electrical and Electronics Blog.

1. AC servomotors and
2. D.C servomotors.

AC Servomotor

The principle of operation of A.C servomotor is similar to that of three-phase induction motor. AC servomotors are generally two-phase squirrel cage induction type motors. The stator has two distributed windings. One is the control winding and the other is the reference winding. These two windings are displaced from each other by 90º as shown in above figure. The voltage applied to the control winding will be 90º out of phase with respect to the voltage applied to the reference winding. The current in the control winding will set up a flux and this flux will be 90º out of phase to the flux set up by the current in the reference winding. Thus, a resultant rotating magnetic flux is setup in the air gap, which sweeps over the stationary rotor. Due to this rotating flux, an e.m.f is induced in the rotor, which in turn produces a circulating current in the rotor. This circulating current in the rotor will now set up a flux (rotor flux) which interacts with the resultant flux produced by the stator and thus a torque is developed on the rotor. The effect of this torque is that the rotor starts rotating in the same direction as the rotating magnetic flux.

Applications of AC Servo Motor

1. AC servo meters are used for low power applications.
2. These motors are widely used in radar, process control systems, robotics, servo mechanisms, computers and machine tools etc.
3. These are also used in self balancing recorders, AC position control systems, tracking and guidance systems.

DC Servo Motor

DC motors which are used in servo systems are called DC servo motors. DC servo motor is essentially an ordinary D.C motor except with few variations in its constructional features. These are used when quick response to control signals and high starting torque is required. The figure shows the layout of DC servo motor.

Working Principle of DC Servo Motor

When an electric current flows through the armature winding, the magnetic field is induced in it. This induced field opposes the field, which is set up by the permanent magnets. The difference in magnetic field produces a torque on the rotor. The torque produced by the rotor will be constant throughout the rotation, as the field strength depends on the function of current. The torque of the D.C servo motor is given as,

\[{{T}_{m}}(t)={{k}_{m}}{{I}_{a}}(t)\]

Where,

T_m — Torque produced

I_a – Armature current

k_m – Motor’s torque constant.

Applications of DC Servo Motor

1. D.C servomotors are used for high power applications.
2. These motors are widely used in instruments, tape drives, printers, robot system, air craft control systems etc.
3. These are also used in electromechanical actuators, process controllers and disk drive.

Difference between AC servomotor and DC servomotor

The post What is Servomotor? Working, Diagram, Types (AC & DC) & Applications appeared first on Electrical and Electronics Blog.

Figure 1: Permanent Magnet Stepper Motor.

Construction of Permanent Magnet Stepper Motor

The stator of the Permanent Magnet Stepper Motor is similar to that of the variable reluctance stepper motor, whereas the rotor is replaced by a permanent magnet. In this type of stepper motor the stepping angle would be more due to difficulty in manufacturing the rotor with number of poles. The basic structure of a two pole motor is as shown in figure 1.

Working of Permanent Magnet Stepper Motor

In the equivalent circuit shown with supply source connected (see Figure 2), the current flows in the forward direction, when phase A is energized with A-north and A’-south the position of rotor is as shown in the figure. When phase B is energized with B-north and B’-south the rotor rotates in clockwise direction with an angular shift of β i.e., 60º and again it moves 60º when C phase is energized. After the rotation of 120º, if again phase A is fed supply, then the rotor moves in the anticlockwise direction due to the repulsive force between the like poles.

In order to keep the rotation in same direction, it is required to change the polarity either by interchanging the winding coil terminals or by changing the supply source. The circuit shows the method of changing the source terminals. This change in current should be done after every k angle of rotation.

\[k=\frac{360{}^\circ }{\text{Number of phases}}\]

This motor is also called as variable speed brushless D.C motor.

The post What is Permanent Magnet Stepper Motor? Working, Diagram & Construction appeared first on Electrical and Electronics Blog.

Figure 1.

For pure metals, the resistance increases linearly with increase in temperature as shown in Fig. 1.8.2, and for a certain range of temperature (typically 0 to 100ºC) the rate of increase of resistance (slope of the line) remains constant. The resistance of metals reduces with reduction in temperature and it reduces to 0 Ω at a temperature of -234.5ºC as shown in Fig. 1.

Resistance Temperature Coefficient (R.T.C.):

Figure 2.

Consider a conductor having an increasing resistance linearly with temperature as shown in Fig. 2.

Let,

R₀ – Resistance at 0ºC

R₁ – Resistance at t₁ºC

R₂ – Resistance at t₂ºC

Definition :

The resistance temperature coefficient (RTC) at tºC is defined as the ratio of change in resistance of the material per degree Celsius to its resistance at tºC.

It is denoted by α_t and its units are per degree Celsius (/ºC).

\[\text{RTC at t}{}^\circ \text{C = }{{\alpha }_{t}}=\frac{\text{ }\!\!\Delta\!\!\text{ R per  }\!\!{}^\circ\!\!\text{ C}}{{{\text{R}}_{\text{t}}}}\]

Where,

ΔR – Change in resistance

R_t – Resistance at tºC

R.T.C. at 0ºC :

The R.T.C. at 0ºC is denoted by α₀ and it is defined as follows :

\[{{\alpha }_{0}}=\frac{\text{Change in resistence per  }\!\!{}^\circ\!\!\text{ C}}{\text{Resistence at 0 }\!\!{}^\circ\!\!\text{ C}}\]

The change in resistance per ºC is equal to the slope of the characteristics shown in Fig. 1.9.1.

α₀ = Slope of the characteristic/R₀

\[{{\alpha }_{0}}=\frac{({{R}_{2}}-{{R}_{1}})/({{t}_{2}}-{{t}_{1}})}{{{R}_{0}}}\]

R.T.C. at t₁ºC :

The R.T.C. at t₁ºC is denoted by α₁ and it is defined as follows :

\[{{\alpha }_{1}}=\frac{\text{Change in resistance per }{}^\circ \text{C}}{\text{Resistance at }{{\text{t}}_{\text{1}}}{}^\circ \text{C}}\]

\[=\frac{\text{Slope}}{{{\text{R}}_{\text{1}}}}\]

\[{{\alpha }_{1}}=\frac{({{R}_{2}}-{{R}_{1}})/({{t}_{2}}-{{t}_{1}})}{{{R}_{1}}}\]

So in general we can write that the R.T.C. at temperature t_n is given by,

\[{{\alpha }_{n}}=\frac{\text{Slope of the characteristics}}{{{\text{R}}_{\text{n}}}}\]

Where,

R_n = Resistance of the conductor at temperature T_n.

Unit of R.T.C.

We know that,

\[{{\alpha }_{n}}=\frac{\text{Slope of the charecteristics}}{\text{Resistance at }{{\text{t}}_{\text{1}}}{}^\circ \text{C}}\]

\[=\frac{({{R}_{2}}-{{R}_{1}})/({{t}_{2}}-{{t}_{1}})}{{{R}_{n}}}\]

\[=\frac{\Omega /{}^\circ \text{C}}{\Omega }=/{}^\circ \text{C}\]

Thus the R.T.C. is measured in per degree Celsius (/ºC).

Expression for Resistance at tºC

Figure 3.

Consider the R versus temperature characteristics of metal. (Fig. 3).

Let R_t be the value of resistance at tºC.

\[\text{RTC at t}{}^\circ \text{C = }{{\alpha }_{t}}\]

\[=\frac{\text{Slope of the charecteristics}}{{{\text{R}}_{\text{t}}}}\]

\[\text{But slope = }\frac{{{R}_{t}}-{{R}_{0}}}{t-0}=\frac{{{R}_{t}}-{{R}_{0}}}{t}\]

And,

\[{{\alpha }_{0}}=\frac{\left( {{R}_{t}}-{{R}_{0}} \right)/t}{{{R}_{0}}}\]

\[{{\text{ }\!\!\alpha\!\!\text{ }}_{\text{0}}}{{\text{R}}_{\text{0}}}\text{t = }{{\text{R}}_{\text{t}}}-{{\text{R}}_{\text{0}}}\]

\[{{\text{R}}_{\text{t}}}\text{= }{{\text{R}}_{\text{0}}}\text{( 1 + }{{\text{ }\!\!\alpha\!\!\text{ }}_{\text{0}}}\text{t )}\]

We can generalize this expression by replacing t by t₂ and 0 by t₁ to get,

\[{{\text{R}}_{\text{t2}}}\text{= }{{\text{R}}_{\text{t1}}}\text{( 1 + }{{\text{ }\!\!\alpha\!\!\text{ }}_{\text{t1}}}\Delta \text{t )}\]

Where,

Δt = Change in temperature = (t₂ – t₁)

α_t1 = R.T.C. at t₁ºC and R_t2 = Resistance at t₂ºC.

Note :

Hence we conclude that the R.T.C. changes with the change in temperature. Higher the value of R.T.C. and R.T.C is maximum at 0ºC.

The post Temperature Coefficient of Resistance – Definition, Formula, Derivation & Unit appeared first on Electrical and Electronics Blog.

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.

The post Series and Parallel Connection of Batteries – Theory, Diagram & Formula appeared first on Electrical and Electronics Blog.

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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