CURRENT ELECTRICITY

Q-1 WHAT IS ELECTRIC CURRENT?

Electric Current (I)

The rate of flow of charge through any cross-section of a wire is called electric current flowing through it.

Electric current (I) = q / t. 
Its SI unit is ampere (A).

Q-2 WHAT IS CONVENTIONAL DIRECTION?

The conventional direction of electric current is the direction of motion of positive charge.

• The current is the same for all cross-sections of a conductor of non-uniform cross-section.

•  Similar to the water flow, 
• charge flows faster where the conductor is smaller in cross-section and 
• slower where the conductor is larger in cross-section, so that
• charge rate remains unchanged.

If a charge q revolves in a circle with frequency f,
 the equivalent current,

i = qf

(In a metallic conductor current flows due to motion of free electrons while in electrolytes and ionized gases current flows due to electrons and positive ions.)

Types of Electric Current

According to its magnitude and direction electric current is of two types

(i) Direct Current (DC) Its magnitude and direction do not change with time. A ceil, battery or DC dynamo are the sources of direct current.

(ii) Alternating Current (AC) An electric current whose magnitude changes continuously and changes its direction periodically is called alternating current. AC dynamo is source of alternating current.

Current Density

The electric current flowing per unit area of cross-section of conductor is called current density.

Current density (J) = I / A

Its S1 unit is ampere metre-2 and dimensional formula is [AT-2].

It is a vector quantity and its direction is in the direction of motion positive charge or in the direction of flow of current.

Thermal Velocity of Free Electrons

Free electrons in a metal move randomly with a very high speed of the order of 105 ms-1. This speed is called thermal velocity of free electron.

Average thermal velocity of free electrons in any direction remains zero.

Drift Velocity of Free Electrons


https://www.youtube.com/watch?v=qg0JY4GNK0w

When a potential difference is applied across the ends of a conductor, the free electrons in it move with an average velocity opposite to direction of electric field. which is called drift velocity of free electrons.

Drift velocity vd = eEτ / m = eVτ / ml

where, τ = relaxation time, e = charge on electron,

E = electric field intensity, 1 = length of the conductor,

V = potential difference across the ends of the conductor

m = mass of electron.

Relation between electric current and drift velocity is given by

vd = I / An e

Mobility

The drift velocity of electron per unit electric field applied is mobility of electron.

Mobility of electron (μ) = vd / E

Its SI unit is m2s-1V-1 and its dimensional formula is [M-1T2A].

Ohm’s Law

If physical conditions of a conductor such as temperature remains unchanged, then the electric current (I) flowing through the conductor is directly proportional to the potential difference (V) applied across its ends.

I ∝ V

or V = IR

where R is the electrical resistance of the conductor and R = Ane2 τ / ml.

Electrical Resistance

The obstruction offered by any conductor in the path of flow of current is called its electrical resistance.

Electrical resistance, R = V / I

Its SI unit is ohm (Ω) and its dimensional formula is [ML2T-3A-2].

Electrical resistance of a conductor R = ρl / A

where, l = length of the conductor, A = cross-section area and

ρ = resistivity of the material of the conductor.

Resistivity

Resistivity of a material of a conductor is given by

ρ = m / n2 τ

where, n = number of free electrons per unit volume.

Resistivity of a material depend on temperature and nature of the material.

It is independent of dimensions of the conductor, i.e., length, area of cross-section etc.

Resistivity of metals increases with increase in temperature as

ρt = ρo (1 + αt)

where ρo and ρt are resistivity of metals at O°C and t°C and α temperature coefficient of resistivity of the material.

For metals α is positive, for some alloys like nichrome, manganin and constantan, α is positive but very low.

For semiconductors and insulators. α is negative.

Resistivity is low for metals, more for semiconductors and very high alloys like nichrome, constantan etc.

(In magnetic field the resistivity of metals increases. But resistivity of ferromagnetic materials such as iron, nickel, cobalt etc decreases in magnetic field.)

Electrical Conductivity

The reciprocal of resistivity is called electrical conductivity.

Electrical conductivity (σ) = 1 / ρ = 1 / RA = ne2 τ / m

Its SI units is ohm-1 m-1 or mho m-1 or siemen m-1.

Relation between current density (J) and electrical conductivity (σ) is given by

J = σ E

where, E = electric field intensity.

Ohmic Conductors

Those conductors which obey Ohm’s law, are called ohmic conductors e.g., all metallic conductors are ohmic conductor.

For ohmic conductors V – I graph is a straight line.

Non-ohmic Conductors

Those conductors which do not obey Ohm’s law, are called non-ohmic conductors. e.g., diode valve, triode valve, transistor , vacuum tubes etc.

For non-ohmic conductors V – I graph is not a straight line.

Superconductors

When few metals are cooled, then below a certain critical temperature their electrical resistance suddenly becomes zero. In this state, these substances are called superconductors and this phenomena is called superconductivity.

Mercury become superconductor at 4.2 K, lead at 7.25 K and niobium at 9.2 K

Colour Coding of Carbon Resistors

The resistance of a carbon resistor can be calculated by the code given on it in the form of coloured strips.

Colour coding Colour Figure Black 0 Brown 1 Red 2 Orange 3 Yellow 4 Green 5 Blue 6 Violet 7 Grey 8 White 9 Tolerance power Colour Tolerance Gold 5% Silver 10% No colour 20%

This colour coding can be easily learned in the sequence “B B ROY Great Bratain Very Good Wife”.

Combination of Resistors

1.In Series

(i) Equivalent resistance, R = R1 + R2 + R3

(ii) Current through each resistor is same.

(iii) Sum of potential differences across individual resistors is equal to the potential difference, applied by the source.

2. In Parallel

Equivalent resistance

1 / R = 1 /R1 + 1 / R2 + 1 / R3

Potential difference across each resistor is same.

Sum of electric currents flowing through individual resistors is equal to the be electric current drawn from the source.

Electric Cell

An electric cell is a device which converts chemical energy into electrical energy.

Electric cells are of two types

(i) Primary Cells Primary ceUs cannot be charged again. Voltic, Daniel and Leclanche cells are primary cells.

(ii) Secondary Cells Secondary cells can be charged again and again. Acid and alkali accumulators are secondary cells.

Electro – motive – Force (emf) of a Cell

The energy given by a cell in flowing unit positive charge throughout the circuit completely one time, is equal to the emf of a cell.

Emf of a cell (E) = W / q.

Its SI unit is volt.

Terminal Potential Difference of a Cell

The energy given by a cell in flowing unit positive charge through till outer circuit one time from one terminal of the cell to the other terminal of the cell.

Terminal potential difference (V) = W / q.

Its SI unit is volt.

Internal Resistance of a Cell

The obstruction offered by the electrolyte of a cell in the path of electric current is called internal resistance (r) of the cell. Internal resistance of a cell

(i) Increases with increase in concentration of the electrolyte.

(ii) Increases with increase in distance between the electrodes.

(iii) Decreases with increase in area of electrodes dipped in electrolyte.

Relation between E. V and r

E = V + Ir

r = (E / V – 1) R

If cell is in charging state, then

E = V – Ir

Grouping of Cells

(i) In Series If n cells, each of emf E and internal resistance r are connected in series to a resistance R. then equivalent emf

[Image: CBSE Class 11 Physics Notes Current Electricity]  

Eeq = E1 + E2 + …. + En = nE

Equivalent internal resistance req = r1 + r2 + …. + rn = nr

Current In the circuit I = Eeq / (R + req) = nE / (R + nr)

(ii) In Parallel If n cells. each of emf E and internal resistance r are connected to in parallel. then equivalent emf. Eeq = E

Equivalent internal resistance

1 / req = 1 / r1 + 1 / r1 + … + 1 / rn = n / r or req = r / n

Current In the circuit I = E / (R + r / n)

(iii) Mixed Grouping of Cells If n cells, each of emf E and internal resistance r are connected in series and such m rows are connected in parallel, then

Equivalent emf, Eeq

Equivalent Internal resistance req

Current in the circuit, I = nE / (R + nr / m)

or I = mnE / mR + nr

Note Current in this circuit will be maximum when external resistance is equal to the equivalent internal resistance, i.e.,

R = nr / m ⇒ mR = nr

Kirchhoff’s Laws

There are two Kirchhoff’s laws for solving complicated electrical circuits

(i) Junction Rule The algebraic sum of all currents meeting at a junction in a closed circuit is zero, i.e., Σ I = O.

This law follows law of conservation of charge.

(ii) Loop Rule The algebraic sum of all the potential differences in any closed circuit is zero, i.e.,

ΣV = 0 ⇒ ΣE = ΣIR

This law follows law of conservation of energy.

Balanced Wheatstone Bridge

Wheatstone bridge is also known as a metre bridge or slide wire bridge.

This is an arrangement of four resistance in which one resistance is unknown and rest known. The Wheatstone bridge as shown in figure. The bridge is said to be balanced when deflection in galvanometer is zero, i.e., ig = O.

Principle of Wheatstone Bridge

P / Q = R / S

The value of unknown resistance S can found. as we know the value of P,Q and R. It may be remembered that the bridge is most sensitive, when all the four resistances are of the same order.

Meter Bridge

This is the simplest form of Wheatstone bridge and is specially useful for comparing resistance more accurately.

R / S = l1 / (100 – l1)

where l1 is the length of wire from one end where null point is obtained.

Potentiometer

Potentiometer is an ideal device to measure the potential difference between two points. It consists of a long resistance wire AB of uniform cross section in which a steady direct current is set up by means of a battery.

If R be the total resistance of potentiometer wire L its total length, then potential gradient, i.e., fall in potential per unit length along the potentiometer will be

K = V / L = IR / L

= Eo R / (Ro + R)L

where, Eo = emf of battery and Ro = resistance inserted by means of rheostat Rh.

Determination of emf of a Cell using Potentiometer

If with a cell of emf E on sliding the contact point we obtain zero deflection in galvanometer G when contact point is at J at a length I from the end where positive terminal of cell have been joined. then fall in potential along length i is just balancing the emf of cell. Thus, we have

E = Kl

or E1 / E2 = l1 / l2

Determination of Internal Resistance of a Cell using Potentiometer

The arrangement is shown in figure. If the cell E is in open circuit and balancing length l1, then

E = Kl1

But if by inserting key K2 circuit of cell is closed, then ooten difference V is balanced by a length l2 of potential where

V = Kl2

Internal resistance of cell

r = E – V / V , R = l1 – l2 / l2 * R

Important Points

• Potentiometer is an ideal voltmeter.
• Sensitivity of potentiometer is increased by increasing length of potentiometer wire.
• If n identical resistances are first connected in series and then in parallel. the ratio of the equivalent resistance.

Rs / Rp= n2 / 1

• If a skeleton cube is made with 12 equal resistance,each having a resistance R, then the net resistance across

1. The diagonal of cube = 5 / 6 R
2. The diagonal of a face = 3 / 4 R
3. along a side = 7 / 12 R

• If a resistance wire is stretched to a greater length, keeping volume constant, then

R ∝ l2 ⇒ R1 / R2 = (l1 / l2)2

and R ∝ 1 / r4 ⇒ R1 / R2 = (r2 / r1)4

where l is the length of wire and r is the radius of cross-section area of wire.

PERIODIC TABLE

PHYSCIS UNIT

Circuits

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ELECTRICITY

Hypotheses about the origins of life

The Oparin-Haldane hypothesis, Miller-Urey experiment, and RNA world.

Key points:

Q-1 WHEN DID EARTH FORMED?

• The Earth formed roughly $4.5$4, point, 5 billion years ago, and life probably began between $3.5$3, point, 5 and $3.9$3, point, 9 billion years ago.
• The Oparin-Haldane hypothesis suggests that life arose gradually from inorganic molecules, with “building blocks” like amino acids forming first and then combining to make complex polymers.
• The Miller-Urey experiment provided the first evidence that organic molecules needed for life could be formed from inorganic components.
• Some scientists support the RNA world hypothesis, which suggests that the first life was self-replicating RNA. Others favor the metabolism-first hypothesis, placing metabolic networks before DNA or RNA.
• Simple organic compounds might have come to early Earth on meteorites.

Introduction

Q-2 If there were other life out there in the universe, how similar do you think it would it be to life on Earth?

 Q-3 Would it use DNA as its genetic material, like you and me? Would it even be made up of cells?

1. We can only speculate about these questions, since we haven't yet found any life forms that hail from off of Earth.
2.  But we can think in a more informed way about whether life might exist on other planets (and under what conditions) by considering how life may have arisen right here on our own planet.
3. In this article, we'll examine scientific ideas about the origin of life on Earth.

 The when of life's origins ($3.5$3, point, 5 billion years ago or more) is well-supported by fossils and radiometric dating.

1.  But the how is much less understood. In comparison to the central dogma or the theory of evolution, hypotheses about life's origins are much more...hypothetical.
2.  No one is sure which hypothesis is correct – or if the correct hypothesis is still out there, waiting to be discovered.

When did life appear on Earth?

Geologists estimate that the Earth formed around $4.5$4, point, 5 billion years ago. This estimate comes from measuring the ages of the oldest rocks on Earth, as well the ages of moon rocks and meteorites, by radiometric dating (in which decay of radioactive isotopes is used to calculate the time since a rock’s formation).

For many millions of years, early Earth was pummeled by asteroids and other celestial objects. Temperatures also would have been very high (with water taking the form of a gas, not a liquid). The first life might have emerged during a break in the asteroid bombardment, between $4.4$4, point, 4 and $4.0$4, point, 0 billion years ago, when it was cool enough for water to condense into oceans$^1$start superscript, 1, end superscript. However, a second bombardment happened about $3.9$3, point, 9 billion years ago. It’s likely after this final go-round that Earth became capable of supporting sustained life.

The earliest fossil evidence of life

The earliest evidence of life on Earth comes from fossils discovered in Western Australia that date back to about $3.5$3, point, 5 billion years ago. These fossils are of structures known as stromatolites, which are, in many cases, formed by the growth of layer upon layer of single-celled microbes, such as cyanobacteria. (Stromatolites are also made by present-day microbes, not just prehistoric ones.)

Image credit: "Stromatolite," by Didier Descouens, CC BY-SA 4.0.

The earliest fossils of microbes themselves, rather than just their by-products, preserve the remains of what scientists think are sulfur-metabolizing bacteria. The fossils also come from Australia and date to about $3.4$3, point, 4 billion years ago$^2$start superscript, 2, end superscript.

Bacteria are relatively complex, suggesting that life probably began a good deal earlier than $3.5$3, point, 5 billion years ago. However, the lack of earlier fossil evidence makes pinpointing the time of life’s origin difficult (if not impossible).

How might life have arisen?

In the 1920s, Russian scientist Aleksandr Oparin and English scientist J. B. S. Haldane both separately proposed what's now called the Oparin-Haldane hypothesis: that life on Earth could have arisen step-by-step from non-living matter through a process of “gradual chemical evolution.” $^3$start superscript, 3, end superscript

Oparin and Haldane thought that the early Earth had a reducing atmosphere, meaning an oxygen-poor atmosphere in which molecules tend to donate electrons. Under these conditions, they suggested that:

• Simple inorganic molecules could have reacted (with energy from lightning or the sun) to form building blocks like amino acids and nucleotides, which could have accumulated in the oceans, making a "primordial soup." $^3$start superscript, 3, end superscript
• The building blocks could have combined in further reactions, forming larger, more complex molecules (polymers) like proteins and nucleic acids, perhaps in pools at the water's edge.
• The polymers could have assembled into units or structures that were capable of sustaining and replicating themselves. Oparin thought these might have been “colonies” of proteins clustered together to carry out metabolism, while Haldane suggested that macromolecules became enclosed in membranes to make cell-like structures$^{4,5}$start superscript, 4, comma, 5, end superscript.

The details of this model are probably not quite correct. For instance, geologists now think the early atmosphere was not reducing, and it's unclear whether pools at the edge of the ocean are a likely site for life's first appearance. But the basic idea – a stepwise, spontaneous formation of simple, then more complex, then self-sustaining biological molecules or assemblies – is still at the core of most origins-of-life hypotheses today.

From inorganic compounds to building blocks

In 1953, Stanley Miller and Harold Urey did an experiment to test Oparin and Haldane’s ideas. They found that organic molecules could be spontaneously produced under reducing conditions thought to resemble those of early Earth.

Miller and Urey built a closed system containing a heated pool of water and a mixture of gases that were thought to be abundant in the atmosphere of early earth ($\text{H}_{2}$H, start subscript, 2, end subscript$\text{O}$O, $\text{NH}_{4}$N, H, start subscript, 4, end subscript, $\text{CH}_{4}$C, H, start subscript, 4, end subscript, and $\text{N}_{2}$N, start subscript, 2, end subscript). To simulate the lightning that might have provided energy for chemical reactions in Earth’s early atmosphere, Miller and Urey sent sparks of electricity through their experimental system.

Cartoon depiction of the apparatus used by Miller and Urey to simulate conditions on early Earth.

Image credit: "Miller and Urey's experiment," by CK-12 Foundation, CC BY-NC 3.0.

After letting the experiment run for a week, Miller and Urey found that various types of amino acids, sugars, lipids and other organic molecules had formed. Large, complex molecules like DNA and protein were missing, but the Miller-Urey experiment showed that at least some of the building blocks for these molecules could form spontaneously from simple compounds.

Were Miller and Urey's results meaningful?

Scientists now think that the atmosphere of early Earth was different than in Miller and Urey's setup (that is, not reducing, and not rich in ammonia and methane)$^{6,7}$start superscript, 6, comma, 7, end superscript. So, it's doubtful that Miller and Urey did an accurate simulation of conditions on early Earth.

However, a variety of experiments done in the years since have shown that organic building blocks (especially amino acids) can form from inorganic precursors under a fairly wide range of conditions$^8$start superscript, 8, end superscript.

[What about nucleotides?]

$^9$start superscript, 9, end superscript

From these experiments, it seems reasonable to imagine that at least some of life's building blocks could have formed abiotically on early Earth. However, exactly how (and under what conditions) remains an open question.

From building blocks to polymers

How could monomers (building blocks) like amino acids or nucleotides have assembled into polymers, or actual biological macromolecules, on early Earth? In cells today, polymers are put together by enzymes. But, since the enzymes themselves are polymers, this is kind of a chicken-and-egg problem!

Monomers may have been able to spontaneously form polymers under the conditions found on early Earth. For instance, in the 1950s, biochemist Sidney Fox and his colleagues found that if amino acids were heated in the absence of water, they could link together to form proteins$^{10}$start superscript, 10, end superscript. Fox suggested that, on early Earth, ocean water carrying amino acids could have splashed onto a hot surface like a lava flow, boiling away the water and leaving behind a protein.

Image credit: "Kusový montmorillonit," by Jan Kameníček, CC BY-SA 3.0.

Additional experiments in the 1990s showed that RNA nucleotides can be linked together when they are exposed to a clay surface$^{11}$start superscript, 11, end superscript. The clay acts as a catalyst to form an RNA polymer. More broadly, clay and other mineral surfaces may have played a key role in the formation of polymers, acting as supports or catalysts. Polymers floating in solution might have hydrolyzed (broken down) quickly, supporting a surface-attached model$^{12}$start superscript, 12, end superscript.

The image above shows a sample of a type of clay known as montmorillonite. Montmorillonite in particular has catalytic and organizing properties that may have been important in the origins of life, such as the ability to catalyze formation of RNA polymers (and also the assembly of cell-like lipid vesicles)$^{13}$start superscript, 13, end superscript.

What was the nature of the earliest life?

If we imagine that polymers were able to form on early Earth, this still leaves us with the question of how the polymers would have become self-replicating or self-perpetuating, meeting the most basic criteria for life. This is an area in which there are many ideas, but little certainty about the correct answer.

The "genes-first" hypothesis

One possibility is that the first life forms were self-replicating nucleic acids, such as RNA or DNA, and that other elements (like metabolic networks) were a later add-on to this basic system. This is called the genes-first hypothesis$^{14}$start superscript, 14, end superscript.

Many scientists who subscribe to this hypothesis think that RNA, not DNA, was likely the first genetic material. This is known as the RNA world hypothesis. Scientists favor RNA over DNA as the first genetic molecule for several reasons. Perhaps the most important is that RNA can, in addition to carrying information, act as a catalyst. In contrast, we don’t know of any naturally occurring catalytic DNA molecules$^{15,16}$start superscript, 15, comma, 16, end superscript.

RNA catalysts are called ribozymes, and they could have played key roles in the RNA world. A catalytic RNA could, potentially, catalyze a chemical reaction to copy itself. Such a self-replicating RNA could pass genetic material from generation to generation, fulfilling the most basic criteria for life and, potentially, undergoing evolution. In fact, researchers have been able to synthetically engineer small ribozymes that are capable of self-replication.

[Relics of the RNA world in present-day cells?]

It’s also possible that RNA wasn’t the first information-carrying molecule to serve as genetic material. Some scientists think that an even simpler “RNA-like” molecule with catalytic and information-carrying capacity might have come first, and might have catalyzed or acted as a template for RNA synthesis. This is sometimes called the "pre-RNA world" hypothesis$^{17}$start superscript, 17, end superscript.

The "metabolism-first" hypothesis

An alternative to the genes-first hypothesis is the metabolism-first hypothesis, which suggests that self-sustaining networks of metabolic reactions may have been the first simple life (predating nucleic acids)$^{14,18}$start superscript, 14, comma, 18, end superscript.

These networks might have formed, for instance, near undersea hydrothermal vents that provided a continual supply of chemical precursors, and might have been self-sustaining and persistent (meeting the basic criteria for life). In this scenario, initially simple pathways might have produced molecules that acted as catalysts for the formation of more complex molecules$^{18}$start superscript, 18, end superscript. Eventually, the metabolic networks might have been able to build large molecules such as proteins and nucleic acids. Formation of "individuals" enclosed by membranes (separate from the communal network) would have been a late step$^{14}$start superscript, 14, end superscript.

What might early cells have looked like?

A basic property of a cell is the ability to maintain an internal environment different from the surrounding environment. Today’s cells are separated from the environment by a phospholipid bilayer. It’s unlikely that phospholipids would have been present under the conditions in which the first cells formed, but other types of lipids (ones that would have more likely been available) have also been shown to spontaneously form bilayered compartments$^{19}$start superscript, 19, end superscript.

In principle, this type of compartment could surround a self-replicating ribozyme or the components of a metabolic pathway, making a very basic cell. Though intriguing, this type of idea is not yet supported by experimental evidence – i.e., no experiment has yet been able to spontaneously generate a self-replicating cell from abiotic (non-living) components.

Another possibility: Organic molecules from outer space

Organic molecules might have formed spontaneously from inorganic ones on early Earth, à la Miller-Urey. But could they instead have come from space?

The idea that organic molecules might have traveled to Earth on meteorites may sound like science fiction, but it's supported by reasonable evidence. For example, scientists have found that organic molecules can be produced from simple chemical precursors present in space, under conditions that could exist in space (high UV irradiation and low temperature)$^{20}$start superscript, 20, end superscript. We also know that some organic compounds are found in space and in other star systems.

Most importantly, various meteorites have turned out to contain organic compounds (derived from space, not from Earth). One meteorite, ALH84001, came from Mars and contained organic molecules with multiple ring structures. Another meteorite, the Murchison meteorite, carried nitrogenous bases (like those found in DNA and RNA), as well as a wide variety of amino acids.

Image credit: "ALH84001 meteorite, on display at Smithsonian Museum of Natural History," by J. L. Stuby, CC BY-SA 3.0.

One meteorite that fell in 2000 in Canada contained tiny organic structures dubbed "organic globules." NASA scientists think this type of meteorite might have fallen to Earth often during the planet's early history, seeding it with organic compounds$^{21}$start superscript, 21, end superscript.

[Could life itself have come from elsewhere in the universe?]

Summary

How life originated on our planet is both a fascinating and incredibly complex question. We know roughly when life began, but how remains a mystery.

• Miller, Urey, and others showed that simple inorganic molecules could combine to form the organic building blocks required for life as we know it.
• Once formed, these building blocks could have come together to form polymers such as proteins or RNA.
• Many scientists favor the RNA world hypothesis, in which RNA, not DNA, was the first genetic molecule of life on Earth. Other ideas include the pre-RNA world hypothesis and the metabolism-first hypothesis.
• Organic compounds could have been delivered to early Earth by meteorites and other celestial objects.

These are not the only scientific ideas about how life might have originated, nor are any of them conclusive. Keep your ears (and your mind) open as new information becomes available and new scientific ideas are proposed concerning life's origins.