Electrical circuit, Thermoelectric effect and Chemical effect of current

Kirchhoff’s of current law:

 It states that in any network of the conductors, the algebraic sum of currents meeting at a point is zero. In the other hand it is simply means that the total current leaving a junction is equal to the total current entering that junction

Explanation: let us consider 5 currents meeting t a junction P of the network as shown in figure.

Figure:

Let us adopt the following sign conversions for determine the algebraic sign of different currents. All current entering the junction would be taken as positive whereas those leaving it would be taken as negative. a/c to the above convention, I1 and I4 would be taken as positive whereas I2, I3 and I5  would be taken as negative. Using Kirchhoff’s of current law we have,

I1+(-I2)+(-I3)+I4 +(-I5)=0

Or, ∑I=0

Also, taking the negative of the expression on one side and positive sign on other side,

I1+ I4=I2+I3+I5

Incoming current =outgoing current

Iin=Iout.

Kirchhoff’s Second law: it states that the algebraic sum of all IR drops and EMF in any close loop of network is zero.∑IR${\sum }^{\mathrm{I}\mathrm{R}}$ =∑EMF=0${\sum }^{\mathrm{E}\mathrm{M}\mathrm{F}}=0$

Explanation: let us consider a complex circuit given below to find the current at the various part of the circuit we use Kirchhoff’s law. Let us consider the direction of emf and current flow in anticlockwise direction is taken as positive and clockwise direction as negative.

A/c to second law of Kirchhoff’s, we have∑IR${\sum }^{\mathrm{I}\mathrm{R}}$ =∑EMF${\sum }^{\mathrm{E}\mathrm{M}\mathrm{F}}$

For the closed loop PQRSA,

(+E’)+(-E”) = (+I’)R’+(-I”)R”

Or,  E’-E”=I’R’-I”R”

Similarly for closed loop SRUTS

E” –E’” = I”R”-I”’ R”’

Also from first ale of Kirchhoff’s, we also have ∑I${\sum }^{\mathrm{I}}$=0 ans from sign convention we have

I”’=I” +I’.

Wheat stone bridge’s principle:

It is an electronic device which measure accurate resistance of the conductor. it measure unknown resistance with the help of known resistance. Let P, Q and R are three known resistance and X be the unknown resistance are connected in quadrilateral closed electric circuit and the two junction of the quadrilateral are connected with battery and the remain two junction are connected galvanometer and the deflection was not shown by the galvanometer. These conditions called balance condition.

At this condition,

Ig= 0.at this condition

PQ=$\frac{\mathrm{P}}{\mathrm{Q}}=$XR$\frac{\mathrm{X}}{\mathrm{R}}$

Determination for the balanced condition for the bridge: to determine the balance condition the arrangement are shown in figure.

Let us consider the 4 resistance in are arrange in quadrilateral from when it is connected with battery then current is divided into two part i.e I1 and I3 passes through the resistance P and Q. similarly I2 and I4 are passes through resistance X and R respectively.

From second law of Kirchhoff’s law for the closed loop ADBA we have

I’P + IgRg= I”X……………..1

Similar for closed loop BDCB we have,

I”’ Q = IgRg + I””R………2

Again from first law of Kirchhoff’s at point D

I” + Ig=I””………3

Similarly at B we have

I’ = Ig +I’”………………4

Now at balance condition Ig=0 and no current passes through the galvanometer then above equation 1, 2, 3, and 4. Become.

I’P = I”X……………..5

I”’ Q =  I””R………6

I” =I””………7

I’ = I’”………………8

Dividing eq. 5 by 6 we have

I′QI′′P=l′′Xl′′′′P$\frac{{\mathrm{I}}^{\prime }\mathrm{Q}}{{\mathrm{I}}^{″}\mathrm{P}}=\frac{{\mathrm{l}}^{″}\mathrm{X}}{{\mathrm{l}}^{⁗}\mathrm{P}}$ ……..9

Now from equation from 7, 8, and 9 we have

• =XR$\frac{\mathrm{X}}{\mathrm{R}}$.

This is the expression for the balance condition of the Wheatstone bridge.

P.O Box:

The P.O Box works on the principal of Wheatstone bridge to identify resistance of unknown wires. No. a very low resistance is not measured by P.O box.

Potentiometer:

Potentiometer is electrical sensitive device which is use for following purpose

a. To measure emf and internal resistance of cell.

b. To compare emf of two cells and p.d between two point of circuit and

c. To measure current and resistance accurately of given circuit.

Principle of potentiometer:

It state that when the current is passes through the conductor having uniform crossectional area then the potential drop(V) on any part of the wire is proportional to its length (L) at balance condition. I.e.  V α L.

A potentiometer is preferred to a voltmeter because of the following reasons:

a. If we prefer voltmeter to measure the e.m.f. of a cell voltmeter will not give the correct value of e.m.f. because voltmeter will draw some current from the cell. The circuit is not open and the reading shown by the voltmeter will be the terminal potential difference, e.m.f.

But if we prefer potentiometer to measure the e.m.f.galvanometer shows null deflection in this case no current is drawn from the cell and the cell is in open circuit hence corresponding voltage will be the e.m.f.

b. If we taking the reading with a voltmeter, deflection of the needle is read, but if we take with potentiometer null deflection is taken. So, error in the measurement with voltmeter will be larger than with a potentiometer.

The potentiometer wire can be of cooper but should be of uniform cross-section. If the cross section of potentiometer wire is not uniform, then potential gradient will not be same at all places on the potentiometer wire. Consequently, the measured value of potential difference will not be correct.

Internal resistance:

The resistance offered by the conducting material when current is passing through it called internal resistance. The internal resistance of the cell is the resistance offered by the electrolyte lying between the electrodes of cell when electric current flow through it.

Determination of internal resistance of cell:

The internal resistance of the cell is determining by using the potentiometer. Let us consider a cell of emf E connected with the potentiometer whose internal resistance (r) is to be determining is given below.

The positive terminal of E is connected to point A where the positive terminal of driving cell is connected and negative terminal to galvanometer. A resistance box R is connected with parallel to the cell with key. A steady current is passed through the wire by the drving cell.

First of all the key K is open and the emf E of cell is balanced in wire of potentiometer. Let the balanced point obtained at S and the length from A to S is L1. Then E is balance by p.d VAS i.e. E=VAS

A/c to principle of the potentiometer V α L then, E α L1………….1

Since the resistance R is provided by R.B and the key is closed. A current I1 will pass in the closed circuit of E and R. then a terminal p.d V is obtained across the cell which is again balanced by the p.d in the potentiometer wire. Let S’ be the point at which null deflection is obtained and p.d. across AS’ be VAS’ so, V = VAS’

If L2 is the length of the portion AS’ of the potentiometer wire

VAS’ α L2

V α L2………….2

Dividing 1 by 2 we get

EV=L1L2$\frac{\mathrm{E}}{\mathrm{V}}=\frac{{\mathrm{L}}_1}{{\mathrm{L}}_2}$……..3

As we E=I1( R +r) and V=I1R on putting the value in equation we get

R+rR=L1L2$\frac{\mathrm{R}+\mathrm{r}}{\mathrm{R}}=\frac{{\mathrm{L}}_1}{{\mathrm{L}}_2}$

rR+1=L1L2$\frac{\mathrm{r}}{\mathrm{R}}+1=\frac{{\mathrm{L}}_1}{{\mathrm{L}}_2}$

Or, r = R(……..4

Comparison of emf of two cells:

let us consider two cell having emf E’and E” connected with potentiometer for comparison of emf as shown in figure.

Let E be the emfmantian a stedy current in potentiometer circuit ML.we connected the positive terminal of the E’and E” are joint to point M , the positive terminal of E and negative terminal is connected to the key .a galvanometer are connected between the key and the jokey that move over the potentiometer wire .  Where  E is greater than E’ and E”.

Let us consider one cell E’ is connected in the circuit by closing K’ and E” is open by K”. The key is slid along wire between AB to find the null point. When the jockey at P near to the A on the wire, the length of portion AP is smaller and hence the potential difference is also smaller. Since the emf E’ is grater then VAP and current flow through the galvanometer and deflection occur in the opposite direction.

Again when the jockey is placed at Q near the B. then the potential difference will grater VAP  of portion BQ and current flow through the galvanometer and deflection occur in the opposite direction. This shows that the circuit is correct. on moving jockey we find a point R at which the galvanometer show null deflection at this condition the potential difference at R is equal to E’ and no current flow and there is no develop p.d in the internal resistance of E’ and in galvanometer and the whole emf  E’ is balanced by the p.d VAR by the jokey moving length L’  so, at the balanced condition,

E’=VA

a/c to principle of potentiometer E’ α L’ ……………….1

similarly if the process is repeated for next cell E” and we have E”α L”……….2

Now from 1 and 2 we have

E′E′′=l′l′′$\frac{{\mathrm{E}}^{\prime }}{{\mathrm{E}}^{″}}=\frac{{\mathrm{l}}^{\prime }}{{\mathrm{l}}^{″}}$ or E’ = l′l′′$\frac{{\mathrm{l}}^{\prime }}{{\mathrm{l}}^{″}}$E’’ on knowning the potential E” and measuring the length of the L’ and L”.

We can find E’ from that relation.

Thermoelectric effect

When two wire of different material are joint to form closed circuit and the two jointed end are placed at different temperature then a small emf is develop in that closed circuit and small current flow through the closed circuit this process is called seebeck’s effect or thermoelectric effect.

A couple of wires of dissimilar metals forming a loop and producing thermoelectricity is called thermocouple. The magnitude of emf produced and the direction of current depends on the pair of metals selected from the thermoelectric series and temperature of the junction. In iron – copper thermocouple, current flows from iron to copper at the cold junction. The direction of current flow changes if heating and cooling of the junction are reversed.

The production of electricity by keeping the junction of two dissimilar metals at different temperatures is called thermoelectric effect. The emf thus produced across the junction is called thermo emf and the current obtained from the thermo emf is called thermoelectric current.

The two factors on which thermoelectric e.m.f.produce in a thermocouple depends on are given below:

1. Nature of two metals forming the thermocouple and

2. Temperature difference between two junctions of the thermocouple.

Neutral temperature:

The temperature of hot junction at which the thermo emf generated in the thermocouple becomes maximum is called neutral temperature. It depends on the nature of the materials of the thermo couple.

The uses of thermoelectric effect:

(i) It is used to make solid – state refrigerator device.

(ii) It is used to sense temperature difference.

(iii) It is used to convert thermal energy directly into electricity.

Difference between Thomson effect and Joules heating effect:

Thomson’s effect	Joule’s effect
(i) It is reversible.	It is not reversible.
(ii) Heat is evolved or absorbed.	Heat is always evolved.
(iii) A temperature difference is required along the length of the conductor.	Number temperature difference is required.
(iv) It depends upon the direction of current.	It is independent of direction of the current.

Variation of thermo emf with temperature

 For explanation of the variation of the thermo emf with temperature

 Let us consider iron-copper thermocouple as given below.

Also consider one junction (P) is put in oil bath and another junction (Q) is put in melting ice. If we increase the temperature of oil bath after certain time the temperature of the both junction is same and galvanometer don’t show any deflection and hence no emf is produce. On continuous increasing the temperature of the oil bath by making cold junction at constant, then the deflection of the galvanometer also increases. This shows that thermo emf increase until it attained maximum value and the temperature at which thermo emf become maximum is called neutral temperature. Let ɵn be the temperature at which thermo emfbecome maximum. If we increase the temperature of oil bath beyond the nutral temperature then the thermo emf start to decrease and become zero. Let (ɵi) be the temperature at which thermo emf is zero and this temperature is called temperature of inversion.

The variation of thermo emf with temperature ɵ is given by

E=ɵα+ βθ22$\frac{\beta {\theta }^2}{2}$ Where α and β are constant whose value depend upon the material of conductor and temperature difference of two junction.

Let ɵC be the temperature of the cold junction then,

ɵi- ɵn= ɵn- ɵC

or, ɵn=θc+θi2$\frac{{\theta }_c+{\theta }_i}{2}$

so the neutral temperature lies between the inversion temperature and temperature of cold junction

Thermocouple:

When two wire of different material are joint to form closed circuit and the two joined end are placed at different temperature then a small emf is develop in that closed circuit and small current flow through the closed circuit this process is called seebeck’s effect or thermoelectric effect.

A couple of wires of different metals forming a loop and producing thermoelectricity is called thermocouple. Yes they are constant for the given material.

Figure:

Figure show thermocouple of iron-copper, here current flow from iron to copper wehnt the end is at cold. If we interchange the end i.e. placing cold end in hot region and hot end at cold region the direction of the current is also change.

Neutral temperature: the temperature of hot junction at which the thermo emf becomes maximum is called neutral temperature.

Temperature of inversion: the temperature of the hot junction at which the thermo emf is zero and reverses the direction is called temperature of inversion.

Neutral temperature:

The temperature of hot junction at which the thermo emf becomes maximum is called neutral temperature.

Temperature of inversion:

The temperature of the hot junction at which the thermo emf is zero and reverses the direction is called temperature of inversion.

Relation between Neutral temperature and Temperature of inversion:

If θC be the temperature of cold junction and θi is the temperature of inversion, then it is found that,

Or, θn= θi+θc2$\frac{{\theta }_i+{\theta }_c}{2}$

Similarly, At the neutral temperature,

Or, dedθ$\frac{\mathrm{d}\mathrm{e}}{\mathrm{d}\theta }$ = 0, i.e a + 2bθn = 0

So, θn = a2b$\frac{\mathrm{a}}{2\mathrm{b}}$

Peltier effect:

When current flows through the junctions of two dissimilar metals in the form of closed circuit, heat is absorbed at one junction and evolved on the other junction this effect is called peltier effect.

Causes: When two dissimilar metals are kept in contact, electron flows from one metal to another creating contact potential difference across the junction i.e. one metal will be positive and other negative. When current flows through the circuit, current flows from positive to negative at a junction and negative to positive at the other junction. Energy is absorbed at the junction, at which current flows from negative to positive. Thus, the junction will cool. Similarly, at the other junction energy is given. Thus heat is evolved.

Thomson effect:

When two ends of a metal conductor is maintained at different temperatures and current is passed through it, heat is evolved or absorbed from the conductor. This effect is called Thomson’s effect. The evolution and absorption of heat depends upon the direction of current. There are two types of Thomson effects the positive and negative.

Causes: The distribution of free electrons is uniform in a conductor. If there is temperature difference between two ends, it creates potential difference across the conductor. If current flows from the end of higher potential to lower potential heat is evolved. Similarly, if current flows from the end at lower potential to higher heat is absorbed.

Different between petlier effect and Seeback- effect:

Petlier effect When two wire of different material are joint to form closed circuit and the two jointed end are placed at different temperature then a small emf develops in that closed circuit and small current flow through the closed circuit this process is called seebeck’s effect or thermoelectric effect.	Seeback –effect The Peltier effect is a temperature difference created by applying a voltage between two electrodes connected to a sample of semiconductor material. This phenomenon can be useful when it is necessary to transfer heat from one medium to another on a small scale.
In this effect ,heat energy absorbed from external source is converted into electrical energy	In this effect, one junction evolves heat, whereas the other junction absorbs heat.
When difference of temperature is maintained between the two junction or at a joint point of a thermocouple, the Peltier'se.m.f. is developed	Seebeck effect is the resultant of peltier's effect and Thomson effect.
Peltier-effect devices are used for thermoelectric cooling in electronic equipment and computers when more conventional cooling methods are impractical.	This effect can be used to generate electricity, measure temperature or change the temperature of objects.

Chemical effect of current

Electrolysis:

The process of decomposition of an electrolyte into its constituent ions by the passage of electric current is called electrolysis.

Uses:

(ii) It is used for purification uses of electrolysis are:

(i) It is used for electroplating of chemicals.

(iii) It is used for the manufacture of chemicals.

(iv) It is used for the purpose of medical use.

(v) It is used in printing industry.

First law of electrolysis: it state that mass of the substance liberated or deposited at electrode in electrolysis process is proportional to the quantity of electric charge passed through the solution(electrolyte or system).

If m be the mass of the substance deposit at cathode when Q amount of charge is pass on solution.

Then m α Q

Or, m=ZQ where Z is called proportionality constant called electrochemical equivalent of the given substance.

Or, m=ZIt where Q=It

Experimental verification of the first law of electrolysis

The experimental verification of the faraday’s first law was verified by the above arrangement.

For the constant current:

Cathode plate was placed inside the voltmeter after cleaning, washing ,drying and weighting then the current is passed on the solution for a particular time suppose t1 as shown in figure and the cathode plat was again weighted after passing the current let the deposited copper at cathode is m1.

Again the same current is passing for other particular time t2 and the deposited mass is m2.

Then we have

m1m2$\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}$=t1t2$\frac{{\mathrm{t}}_1}{{\mathrm{t}}_2}$ or, m α t ………………..1

 For the constant time: let m1 and m2 be the mass deposit at the cathode plate at for the same in travel of time by passing varying current I1 and I2 in the above arrangement then we have

m1m2$\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}$=I1I2$\frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}$ or, m α t……………..2

From eq. 1 and 2 we have, m α It  

                                           Or, m α It 

                                             Or, m α Q   where (Q=It)…………3

Here eq. 3 is faraday’s first law of electrolysis and say that ion deposit at cathode is directly proportional to amount of the charge passes through solution.

Second law of electrolysis:

It state when same amount of electric charge passes through different solution (electrolyte or system) then the mass of the substance deposit or liberated at electrode is directly proportional to their chemical equivalents.

If m1, m2, m3, m4, m5 be the masses liberated in different voltmeter  when same current is passes through them and  E1, E2, E3, E4, E5 be chemical  equivalent respectively. Then we have

m1E1$\frac{{\mathrm{m}}_1}{{\mathrm{E}}_1}$=m2E2=m3E3$\frac{{\mathrm{m}}_2}{{\mathrm{E}}_2}=\frac{{\mathrm{m}}_3}{{\mathrm{E}}_3}$=m4E4=m5E5$\frac{{\mathrm{m}}_4}{{\mathrm{E}}_4}=\frac{{\mathrm{m}}_5}{{\mathrm{E}}_5}$   or, mE$\frac{\mathrm{m}}{\mathrm{E}}$ = a constant

Experimental verification of faraday second law of electrolysis

For the experimental verification of second law of faraday’s let us consider silver voltmeter, copper voltmeter and water voltmeter are connected in series as given below.

Figure

If we pass same current for same in travel of time then the mass liberated or deposited on respective cathode is m1, m2, m3 .i.e. Mass deposit at silver cathode is m1, mass deposit at copper electrode is m2 and mass deposit at hydrogen electrode is m3.then, 

m1E1$\frac{{\mathrm{m}}_1}{{\mathrm{E}}_1}$=m2E2=m3E3$\frac{{\mathrm{m}}_2}{{\mathrm{E}}_2}=\frac{{\mathrm{m}}_3}{{\mathrm{E}}_3}$

 Where, E1, E2, E3, be chemical equivalent of silver, copper and hydrogen respectively.

Voltmeter:

It is vessel in which the electrolysis is made of occurs is called voltmeter.

The substances which conduct electricity when dissolved in water are called electrolytes. Acidified water, aqueous solution of salts like NaCl, CuSO4, AgNO3; acids like H2SO4, HCl, HNO3 and bases like NH4OH and KOH are example of electrolyte.

Voltmeter measures the current more accurately because the voltmeter measures the current in terms of mass and electrochemical equivalent (Z) of the substance. Also, it measures the time of the passage of current more accurately. The error in the measurement by the voltmeter is very small in comparison to the ammeter.

Chemical equivalent:

It is the ratio of atomic mass and valency of a substance.

So, Chemical equivalent = Atomicmassvalency$\frac{\mathrm{A}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{c}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}{\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}}$

Electrochemical equivalent

We have, m = zq.

So, z = mq$\frac{\mathrm{m}}{\mathrm{q}}$

If q = 1 colomb, z = m.

Hence, the electrochemical equivalent of a substance is defined as the amount of mass of the substance liberated or deposited in electrolysis when a charge of 1 colomb is passed through the electrolyte of substance.

In SI, m is expressed in kg and q is expressed in colomb(c). Hence, the unit of Z is kgC-1. However, more conviently, the ECE of a substance is expressed in gram per colomb (gC-1).

The quantity of charge required to deposit one gram equivalent (i.e. one chemical equivalent expressed in gram) of any substance is known as faraday. Its value is 96.500 Cml-1.

Primary cell:

A cell in which the chemical reactions are not reversible is called primary cell. When the cell delivers a current, its active material is used up. When the active material is finished, the cell stops delivering current. Now, for the cell to deliver current again, new electrolyte is to be replaced or a new cell is to be used. Due to this reason, the primary cells are expensive. Voltaic cell, dry cell, Lalancehe cell and Daniel cell are example of primary cell.

Secondary cell:

 A cell in which chemical reactions are reversible is called secondary cell. When the cell delivers current, it plates change their chemical composition, the cell plates change all of their chemical composition, the cell is exhausted. The secondary cells are also called storage cells as accumulators. The most common secondary cells are (i) Lead Acid accumulators and (ii) Alkali accumulator.

Difference between primary and secondary cell:

Primary cell.	Secondary cell.
(i) Chemical reaction is irreversible .	Chemical reactions are reversible.
(ii) These cells cannot be recharged	These cells can be recharged.
(iii) These cells have high internal resistance.	These cells have low internal resistance.
(iv) High current are not obtained	High current can be obtained.

Different between Ionic and Electronic conduction:

Ionic conduction	Electronic conduction
Ionic conduction is possible only inside the electrolyte	a. the electronic conduction is possible inside the metallic conductor as well as semiconductor.
The number density (n) of ions in an electrolyte is very small as compared to that of free electrons in a metallic conductor.	The number density (n) of free electrons in a metallic conductor is higher then that of ions in an electrolyte
The drift velocity of ions in ionic conduction is smaller than small of electrons in electronic for a given electric field.	The drift velocity of electron in electronic for a given electric field is greater then that of the ionic conductance.
The resistance offered by the solution to ions in ionic conduction is much more than that offered by the metal to the drifting free electrons in electronic conduction.	The resistance offered by the metal to the drifting free electrons in electric conductionis less than thatof the ionic conduction.

Electrochemical equivalent:

The electrochemical equivalent of a substance is defined as the amount of mass of the substance liberated or deposited in electrolysis when a charge of 1C is passed through the electrolyte of the substance.

The relation between chemical equivalent & electrochemical equivalent:-

Let Q amount of charge is passed through two electrolytes whose chemical equivalents are E1 and E2 and electrochemical equivalent are z1& z2 respectively. If m1& m2 are the masses of the ions liberated or deposited in voltmeter respectively, then we have:

         M1 =z1Q & M2= z2Q

Faraday’s constant:

Faraday’s constant is defined as the amount of charge requires depositing or liberating one mole of monovalent substance during electrolysis. The approximation value of the faraday’s constant is equal to 96500C/mole.

It is given by F= (EQ)/m

Where F= faraday’s constant

E=chemical equivalent of the substance

Q=charge and m=mass of deposit or liberate.