Introduction to Current Electricity
- The motion of charges is called Electric Current.
- The current electricity is the study of the flow of electric charges.
- Alessandro Volta (1745 – 1827) invented the electric battery that generated the first steady flow of electric current.
- The matter is made of atoms.
- Each atom consists of a positively charged nucleus with negatively charged electrons revolving around the nucleus.
- Atoms in metals hold one or more electrons which remain loosely attached to the nucleus.
- These electrons are called free electrons which are easily detached from the atoms.
- The movement or flow of electric charges or electrons over a conductor such as copper wire will constitute an electric current.
- The electric current moves from the positive terminal to the negative terminal via the of a battery.
- The positive terminal is called the higher electric potential and the negative terminal is also called lower electric potential.
- The object or substance that has an abundance of free electrons are called conductors.
- These free electrons move randomly throughout the conductors at a given temperature.
- But there is no net transfer of charges from one end to another end of the conductor, therefore there is no current.
- When the potential difference is applied by the battery across the ends of the conductor, the electrons drift towards the positive terminal of the battery, producing a net electric current (flow of charges).
- Thereby, there is no flow of charges or current in conductor until the potential difference is applied by an external power source such as battery etc.
Electric Current – Definition
- The Electric current is termed as Current generally and has the symbol ‘I’. Therefore ‘I” means electric current.
- The Electric current is said to the rate of flow of charges in a conductor or wire.
- The electric current is the amount of charge moving in any cross-section of a conductor such as a wire in a unit time.
- The net charge ‘Q’ passes via any cross-section of a conductor (wire) in time ‘t’, then the current flowing via the conductor is: I = Q/t.
SI unit of Electric Current
- The SI unit is ampere (A).
- The current passing via a wire is supposed to be one ampere if a charge of one coulomb flows over any cross-section of a wire in one second.
- 1 ampere = 1 coulomb/1 second.
- The electric current is a scalar quantity.
- In an electric circuit, arrows are used to show the direction of the flow of current.
- By convention, the current flow in the electric circuit should be from the positive terminal to the negative terminal of the power source such as a battery.
- The current that is conventional current or simply current which flows in the direction in which positive test charge would move.
- Generally, in circuits, the charges flow are electrons from the negative terminal to the positive terminal of the battery.
- Thereby, the flow of electrons and the direction of conventional current are in the opposite direction.
- Numerically a transfer of positive charge is the equivalent as a transfer of negative charge which points in the opposite direction.
- An electric circuit is a closed conducting loop or path, which has a network of electrical components such as resistor, capacitor, inductor, bulb etc through which electrons flow.
- A simple diagram of an electric circuit has a battery, resistor, electric bulbs, and a switch.
Symbols of Components of a circuit
- Resistor – Used to resist the current, or control the current flowing through a circuit.
- Variable resistor or Rheostat – Used to choose the quantity of the current through a circuit.
- Ammeter – Used to estimate the current in the electric circuit.
- Voltmeter – Used to estimate the potential difference in the electric circuit.
- Galvanometer – Used to show the direction of the current in the electric circuit.
- Diode- Diode has various applications, mostly used in semiconductors.
- Light Emitting Diode (LED) – LED used to emit light.
- Ground Connection – Used to give protection to the electrical components and also works as a reference point to estimate the electric potential.
- If the switch is ‘on’, the bulb glows.
- If the switch is ‘off’, the bulb does not glow.
- The potential difference needed for the flow of charges is supplied by the battery.
- The electrons pass from the negative terminal to the positive terminal of the battery.
- “By convention, the direction of current is taken as the direction of flow of positive charge (or) opposite to the direction of flow of electrons” (Samacheer Kalvi Book #)
- Accordingly, the electric current passes in the circuit from the positive end to the negative end.
Electric Potential and Potential Difference
- A variation in electric potential is required for the movement of electric charges in a wire or conductor.
- In the conductor, the charges will flow from higher electric potential to a lower electric potential.
- The electric potential at a point is described as the amount of work done in driving a unit positive charge from infinity to that point against the electric force.
Electric Potential Difference
- “The electric potential difference between two points is termed as the amount of work done in moving a unit positive charge from one point to another point against the electric force”(Samacheer Kalvi Book #)
- Let us consider, charge Q moved from a point A to another point B.
- Let ‘W’ be the work done for the movement of charge from position A to B.
- The potential difference between the points A and B is V = W/Q
- Where V is the potential difference, W is work done and Q is the charge.
- Potential difference is equivalent to the difference in the electric potential of these two points A and B.
- If VA is the electric potential of A and VB is the electric potential of B.
- Then, the potential difference between point A and B is given by:
- V = VA – VB when VA is more than VB
- V = VB – VA when VB is more than VA
- Electric potential or potential difference’s SI unit is volt (V).
- The potential difference between two points is one volt if one joule of work is done in moving one coulomb of charge from one point to another against the electric force.
- 1 Volt = 1 Joule/ 1 Coulomb
- A German Physicist, Georg Simon Ohm established the relation between the potential difference and current, which is called Ohm’s Law.
- By Ohm’s law, at a constant temperature, the steady current ‘I’ flowing via a conductor is directly proportional to the potential difference ‘V’ between the two ends of the conductor.
- I ∝ V. Hence, I / V = constant.
- The value of proportionality constant is 1/R
- Therefore, I = (1/R) V
- V = IR (By Ohm’s Law)
- R is a constant for a given material (Nichrome) at a given temperature and is known as resistance.
The Resistance of a Material
- Resistance is the property of a material to oppose the flow of charges and the passage of the current through it.
- “Resistance is different for different materials”.
- From Ohm’s Law, V/I = R.
- “The resistance of a conductor is the ratio between the potential difference across the ends of the conductor and the current flowing through the conductor” (Samacheer Kalvi Book #)
Unit of Resistance
- Ω or Ohm is the SI unit of resistance.
- “The resistance of a conductor is one ohm when one ampere current flows through it when a one-volt potential difference is maintained across its ends.” (Samacheer Kalvi Book #)
- 1 ohm = 1 volt / 1 ampere
Electrical Resistivity & Electrical Conductivity
- The resistance of any conductor ‘R’ is directly proportional to the length of the conductor ‘L’ and is inversely proportional to cross-section area ‘A’.
- R ∝ L, R ∝ 1/A,
- Hence, R ∝ L/A
- Therefore, R= ⍴ L/A
- Where ⍴(rho) is a constant, called Electrical Resistivity or Specific Resistance of the Material of the conductor.
- Accordingly, the electrical resistivity of a substance is the resistance of a conductor of unit length and unit area of cross-section and unit is ohm metre.
- Electrical resistivity of a conductor is a measure of the resisting capacity of a specified material to the passage of an electric current.
- It is a constant of a given material.
- Nichrome has the highest resistivity equal to 1.5 x 10-6 Ωm.
- Nichrome is used in making heating elements.
Conductance and Conductivity
- The conductance of the object is numerically expressed as the reciprocal of its resistance R.
- Thereby, the conductance ‘G’ of a conductor is given by G=1/R and its unit is ohm-1
- It is also denoted as ‘mho’.
- The reciprocal of electrical resistivity is called electrical conductivity.
- 𝝈 = 1/⍴
- Conductivity unit is ohm-1 metre-1 or mho metre-1.
- The conductivity is constant for the given material. That means conductance of Iron is the same for all irons whether it is from India or the US.
- Some substances or materials are very good conductors of electricity. Such as Metals.
- Example: Copper, Aluminium, etc
- Some materials are bad conductors of electricity. Such as Non-Metals, Plastic.
- Example: Glass, Rubber, Plastic, Paper, Wood etc.
- Conductivity is more for conductors than the insulator.
- Resistivity is more for an insulator than the conductor.
|Type of Material||Material||Resistivity (Ωm) at 20°C|
|Conductor||Copper||1.62 × 10-8|
|Nickel||6.84 x 10-8|
|Chromium||12.9 x 10-8|
|Insulator||Glass||1010 x 1014|
|Rubber||1013 x 1016|
|Pure water||2.5 x 105|
The resistor is a passive electrical component that has two terminals which provide electrical resistance in the circuit.
Combination of Resistors or System of Resistors
- The combination of the resistors is called the System of Resistors or Grouping of Resistors.
- There are two primary methods in a combination of resistors one series Connection and another one is Parallel Connection
Series Connection of Resistor
- If the resistor is connected end to end, the same current passes through each one of them when connected in series.
- The resistors are connected one after another to form a ‘single-loop’.
- If any part of the circuit is broken, no current passes through. The circuit gets broken as there is only one path.
- Series connection is used in torchlight where one battery is placed after another.
- The sum of the potential difference across the ends of each resistor is given by:
- Rs = R1 + R2 + R3
- The total resistance in the circuit is the sum of resistances of the individual resistors.
- The equivalent resistance in a series connection is higher than the highest of the single resistances.
- Example there are three resistors. R1 = 1, R2 = 2 , R3 = 3. In a series connection, the total resistance is the sum of individual resistors.
- Here Rs = R1 + R2 + R3 , that Rs = 1 + 2 + 3, Rs = 6 Ohm.
Resistances in Parallel
- A parallel circuit has two or more loops through which current passes.
- If the circuit is disconnected in one of the loops, the circuit is disconnected in one of the loops, the current still passes through the other loops.
- The electrification in a house consists of parallel circuits.
- 1/Rp = 1/R1 + 1/R2 + 1/R3
- The equivalent resistance in a parallel combination is less than the lowest of the individual resistances.
- Example there are three resistors. R1 = 1, R2 = 2 , R3 = 3.
- Then 1/Rp = 1/R1 + 1/R2 + 1/R3 , 1/1 + ½ +⅓ = 11/6. Therefore Rs = 6/11 = 0.55 ohms.
Comparison between Series and Parallel connections
|1||Equivalent Resistance||More than the highest resistance||Less than the lowest resistance|
|2||Amount of current||Current is less as effective resistance is more||Current is more as effective resistance is less|
|3||Switching ON/OFF||If one device is disconnected others, do not work||If one device is detached, others will work separately|
- Carbon resistors have a ceramic core, over which a thin coating of crystalline carbon is deposited.
Colour Code for Carbon Resistors
- Carbon resistor consists of a ceramic core on which a thin layer of crystalline carbon is deposited.
- These resistors are inexpensive, stable and compact in size.
- Colour rings are used to indicate the value of the resistance as per certain rules.
- Three coloured rings are employed to symbolise the values of a resistor, the first two rings are important values of resistances, the third ring means the decimal multiplier after them.
- The fourth colour, silver or gold, shows the tolerance of the resistor at 10% or 5%.
- If the fourth ring is absent then the tolerance is 20%.
- Below is the colour-coding table for the resistors
- When reading the value of the resistor, hold the resistor with colour bands to your left.
- Resistor reading never starts with a metallic band on the left.
- For the above resistor, let’s calculate its resistance from its colour code.
- The first digit is 5 (green), the second is 6 (blue), the decimal multiplier is 103 (orange) and tolerance is 5% (gold).
- Thereby, the value of resistance is 56 x 103 Ω or 56 kΩ with tolerance value 5%.
Temperature dependence of Resistivity
- The resistivity of the material is dependent on temperature.
- The resistivity of a conductor increases with the increase in temperature.
- When the temperature of a conductor increases, the average kinetic energy of electrons in the conductor increases. This increases frequent collisions and hence the resistivity increases.
- There also exist non-linear regions at very low temperatures. The resistivity approaches some finite value as the temperature nears absolute zero.
- The conductance increases with increase in temperature for semiconductors.
- This is because as the temperature increases, more electrons will be liberated from their atoms.
- Hence, the current increases and thereby the resistivity decreases.
- A semiconductor with a negative temperature coefficient of resistance is called a thermistor.
- Below table is the values of temperature coefficients of various materials are given:
|Materials||Temperature Coefficient ɑ [°(C)-1]|
|Silver||3.8 x 10-3|
|Copper||3.9 x 10-3|
|Gold||3.4 x 10-3|
|Aluminium||3.9 x 10-3|
|Tungsten||4.5 x 10-3|
|Iron||5.0 x 10-3|
|Platinum||3.92 x 10-3|
|Lead||3.9 x 10-3|
|Nichrome||0.4 x 10-3|
|Carbon||-0.5 x 10-3|
|Germanium||-48 x 10-3|
|Silicon||-75 x 10-3|
The resistivity of materials is:
- Inversely proportional to the number density (n) of the electrons.
- Inversely proportional to the average time between the collision (𝞃 ).
- In metals, if the temperature increases, the average time between the collision (𝞃 ) decreases and n is independent of temperature.
- In semiconductor when temperature increase, n increases and 𝞃 decrease, but an increase in n is dominant than decreasing 𝞃, so overall resistivity decreases.
- The ability of certain metals, their compounds and alloys to conduct electricity with zero resistance at very low temperature is called superconductivity.
- The materials which exhibit this property are called superconductors.
- The phenomenon of superconductors was first observed by Kammerlingh Onnes in 1911 when mercury showed zero resistance at 4.2 K.
- The first theoretical explanation of superconductivity was given by Bardeen, Cooper and Schrieffer in 1957 and it is called the BCS theory.
- The temperature at which electrical resistivity of the material suddenly drops to zero and the material changes from normal conductor to a superconductor is called the transition temperature or critical temperature TC.
- At the transition temperature, the electrical resistivity drops to zero, the conductivity becomes infinity and the magnetic flux lines are excluded from the material.
Applications of Superconductors
- A superconducting generator that small in size and weight can be made for energy savings.
- Superconducting magnets used in bullet trains to levitate the trains above its, which makes trains less heavy, thereby high speed is achieved.
- Used to launch satellite without using rockets, by using superconducting magnetic propulsion.
- High power ore separating machine to be built in future using superconducting magnets that can be used separate tumour cells by high gradient magnetic separation method.
- The superconducting wire can be used for transmission of electricity.
- Can be used as memory devices in electronic devices.
What is the heating effect of electric current?
- Electrical current can generate a potential difference over a resistor, which is connected to that source.
- This potential difference develops a current over the resistor.
- For the constant drawing of current, the source has to continuously use its power.
- A portion of the current from the source can be turned into working and remaining will be turned into heat energy.
- Hence the passage of electric current over wire issues in the generation of heat.
- This event is called the heating effect of current.
- Electric Heater, the Iron box uses this phenomenon to work.
- The heating element used in the electric stove is made of Nichrome.
Joule’s Law of Heating
- Let ‘I’ be the current passing over a resistor of resistance R, and V be the potential difference over the resistor.
- The charge passing over the circuit for a time interval t is Q.
- The work done in transferring the charge Q across the ends of the resistor with a potential difference of V is VQ.
- This energy used by the source gets spent in the resistor as heat.
- Thus, the heat generated in the resistor is:
- H = W = VQ
- As we know the connection in the charge and current is Q = It.
- H = V I t. For Ohm’s law V= IR Therefore we get H = V I t.
- This is understood as Joule’s law of heating.
- Joule’s law of heating states that heat generated in any resistor is:
- “Directly proportional to the square of the current passing through the resistor”. (Samacheer Kalvi Book #)
- “Directly proportional to the resistance of the resistor”. (Samacheer Kalvi Book #)
- “Directly proportional to the time for which the current is passing through the resistor”. (Samacheer Kalvi Book #)
Application of Heating Effect
Electric Heating Device:
- The heating effect due to electric current is utilised in several purposes such as electric iron, electric oven, electric heater, geyser, electric toaster etc.
- These electric heating devices use an alloy of Nickel and Chromium.
- Nickel and Chromium are used because of their high resistivity, high melting point and these cannot be easily oxidized.
- The fuse wire is connected in series in an electric circuit.
- When a massive current passes over the circuit, the fuse wire fuses (melts) because of Joule’s heating effect and the circuit gets cut.
- The circuit and the electrical appliances are saved from damage.
- The fuse wire is made of wire with a low melting point. Example: Tin and Lead Alloy.
Filament in Bulb
- In an electric bulb, where a small spring-like wire is used which is called Filament.
- The filament is made of a material that has a high melting point.
- When a current is passed over this wire, heat is produced. As the melting point is very high and it gets heavily heated.
- This heated element produces Light.
- Mostly Tungsten is used in an electric bulb.
- The electric power is defined as the rate of use of electrical energy.
- It expresses the rate at which the electrical energy is transformed into some other kind of energy.
- Assume a current ‘I’ passes over a wire of resistance R for time t, then the potential difference over the two ends of the wire is V.
- The work done ‘W’ to move the charge over the ends of the wire is given by:
- W = V I t , Power P = Work / Time = VIt/t
- P = VI
- Thus the electric power is the product of the current and potential difference.
Unit of Electric Power
- Watt is the SI unit of electric power.
- Consider a current of 1 Ampere flow over the end of the wire or conductor, with a potential difference of 1 volt, then the electric power is:
- P = 1 Volt x 1 ampere = 1 watt
- Thereby, “one watt is the power consumed when an electric device is operated at a potential difference of one volt and it carries a current of one ampere”. (Samacheer Kalvi Book #)
- Commonly used SI unit of Electric Power is Kilowatt.
- Horse Power (hp) is a unit in the foot-pound-second (fps) or English System. One horsepower is equal to 746 watts.
Electromotive Force and Internal Resistance
- The emf of a battery or cell is the voltage provided by the battery when no current flows in the external circuit.
- The electromotive force determines the amount of work a battery or cell does to move a certain amount of charge around the circuit.
- It is denoted by Symbol ξ, pronounced as Xi.
- An Ideal battery has zero internal resistance and the potential difference across the battery equal to its emf.
- Practically, the battery is made of electrodes and electrolyte, there will be resistance to the flow of charge within the battery. This resistance is called Internal resistance r.
- For a real battery, the terminal voltage is not equal to the emf of the battery.
- A brand new has low internal resistance and increases with ageing.
Cell in Series
- Several cells can be connected to form a battery.
- In a series connection, the negative terminal of one cell is connected to the positive terminal of the second cell.
- Then the negative terminal of the third cell and so on.
- The free positive terminal of the first cell and free negative terminal of the last cell becomes the terminal of the battery.
- Suppose n cells, each of emf ξ volts and internal resistance r ohms is connected in series with an external resistance R.
- Series connection of cells is advantageous only when the effective internal resistance of the cells is negligibly small compared with R.
Cells in Parallel
- In Parallel connection, all the positive terminals of the cells are connected to one point and all the negative terminals to a second point.
- These two points form the positive and negative terminals of the battery.
- The current to the whole battery is the same for the connection of the Parallel cells.
- Hence it is advantageous to connect cells in parallel when the external resistance is very small compared to the internal resistance of the cells.
- Ohm’s law is useful only for simple circuits.
- For complex circuits, Kirchhoff’s rules are used to find current and voltage.
- There are two Kirchhoff rules: one is Kirchhoff’s current rule and another one Kirchhoff’s voltage rule.
Kirchhoff’s First Rule (Current Rule or Junction Rule)
- It states that the algebraic sum of the currents at any junction of a circuit is zero.
- All the charges that enter a given junction in a circuit must leave that junction.
- Current entering the junction is taken as positive and current leaving the junction is taken negatively.
Kirchhoff’s Second Rule (Voltage Rule of Loop Rule)
- It states that in a closed circuit the algebraic sum of the products of the current and resistance of each part of the circuit is equal to the total emf included in the circuit.
- This rule follows from the law of conservation of energy for an isolated system.
- The energy supplied by the emf sources is equal to the sum of the energy delivered to all resistors.
- The product of current and resistance is taken as positive when the direction of the current is followed.
- Kirchhoff voltage rule has to be applied only when all currents in the circuit reach a steady-state condition (the current in various branches are constant).
- It is one of the important applications of Kirchhoff rules.
- It is used to compare the resistance and also helps in determining the unknown resistances in the electrical network.
- The bridge consists of four resistances P, Q, R and S.
- A galvanometer G is connected between points B and D.
- The battery is connected between points A and C.
- The current through the galvanometer is IG and its resistance is G.
- The Wheatstone bridge equation is P/Q = R/S
- It is another form of Wheatstone’s Bridge
- It is used to measure the potential difference.
- Seebeck discovered that in a closed circuit consisting of two dissimilar metals when the junctions are maintained at a temperature and potential difference (emf) is developed.
- The current that flows due to the emf developed is called thermoelectric current.
- The two dissimilar metals connected to form two junctions are known as a thermocouple.
- If the hot and cold junctions are interchanged, the direction of current also reverses. Hence the effect is reversible.
- The magnitude of the emf developed in a thermocouple depends on the nature of metals forming the couple and temperature difference between the junctions.
Application of Seebeck Effect
- The Seebeck effect is used in thermoelectric generators or Seebeck generators. These thermoelectric generators are used in power plants to convert waste heat into electricity.
- This effect is utilized in automobiles as automotive thermoelectric generators for increasing fuel efficiency.
- Seeback effect is used in thermocouples and thermopiles to measure the temperature difference between the two objects.
- In 1834, Peltier discovered, When an electric current is passed through a circuit of a thermocouple, heat is evolved at one junction and absorbed at the other junction.
- This effect is called the Peltier Effect.
- If two points in a conductor are at different temperatures, the density of electrons at these points will differ and as a result, the potential difference is created between these points.
- The Thomson effect is irreversible.
- The Positive Thomson effect is observed in Sb, Ag, Zn, Cd etc.
- And the Negative Thomson effect is observed in Pt, Bi, Co, Ni, Hg etc.
- In the case of lead, the Thomson effect is nil.
Thomson Coefficient (𝝈)
- The amount of heat energy absorbed or evolved when one-ampere current flows for one second (one coulomb) in metal between two points which differ in temperature by 1°C is called the Thomson coefficient.
- It is denoted by 𝝈. Its unit is volt per °C.
Magnetic Effect of Current
- In 1820, Danish Physicist, Hans Christian Oersted observed that current through a wire caused a deflection in a nearby magnetic needle.
- This indicates that the magnetic field is associated with a current-carrying conductor.
- Magnetic Induction due to an infinitely long straight conductor carrying current is B = 𝞵0 I / 2𝞹a.
- If the conductor is placed in a medium of permeability, 𝞵
- B = 𝞵I / 2𝞹a.
Drift Velocity and Mobility
- Drift Velocity is the velocity with which free electrons get drifted towards the positive terminal when an electric field is applied.
- If ꞇ is the average time between two successive collisions and the acceleration experienced by the electrons be a, then the drift velocity is given by,
Vd = a ꞇ
- 𝝁 = eꞇ / m is the mobility and is defined as the drift velocity acquired per unit electric field.
- Its SI unit is m2V-1s-1.
- The drift velocity of electrons is proportional to the electric field intensity.
- It is very small and is of the order of 0.1 cm s-1.
- Current density at a point is defined as the quantity of charge passing per unit time through the unit area, taken perpendicular to the direction of flow of charge at that point.
- The current density J for a current I flowing across a conductor having an area of cross-section A is: J = (q/t) / A
- J = I / A
- Current density is a vector quantity and expressed in Am-2.
- Tangent Galvanometer is a device used for measuring current.
- It needs to be adjusted to be between 30° and 60° since the tangent galvanometer is most sensitive at a deflection of 45°.
Pointer type moving coil Galvanometer
- The suspended coil galvanometers are very sensitive. It can measure the current of the order of 10-8 ampere.
Conversion of Galvanometer into an Ammeter
- A Galvanometer is a device used to detect the flow of current in an electrical circuit.
- However, a galvanometer is converted into an ammeter by connecting a low resistance in parallel with it.
- As a result, when large current flows in a circuit, only a small fraction of the current passes through the galvanometer and the remaining larger portion of the current passes through the low resistance.
- The low resistance connected in parallel with the galvanometer is called shunt resistance.
- The scale is marked in Ampere.
- Ra is very low and this explains why an ammeter should be connected in series.
- When connected in series, the ammeter does not appreciably change the resistance and current in the circuit.
- Hence the ideal ammeter is one which has zero resistance.
Conversion of Galvanometer into Voltmeter
- A Galvanometer can be converted into a voltmeter by connecting a high resistance in series with it.
- The scale is calibrated in volt.
- RV is very large, and hence a voltmeter is connected in parallel in a circuit as it draws the least current from the circuit.
- Samacheer Kalvi Book. Standard Ten – Science. First Edition ed., vol. I, Government of Tamil Nadu – Department of School Education, 2019. Department of School Education, http://tnschools.gov.in/textbooks. Accessed 29 10 2020.